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705 


ENGINEERING 
LIBRAP 


THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

LOS  ANGELES 


GIFT  OF 

BALDWIN  M.  WOODS 


THE  AIR   PROPELLER 

Its  working  characteristics  and  theory, 
together  with  a  brief  discussion  of  the 
airplane  engine  and  the  power  availa- 
ble for  airplane  propulsion 


BY 

FREDERICK  BEDELL,  PH.D. 

Professor  in  Physics,  Cornell  University 
Author  of  Airplane  Characteristics,  etc. 

Member  Aeronautical  Society  of  America,  Past  Vice-President 
American  Institute  of  Electrical  Engineers,  Fellow  and  Past 
General  Secretary  American  Association  for  the  Advancement 
of  Science,  Member  the  American  Physical  Society  and  Manag- 
ing Editor  of  The  Physical  Review. 


ILLUSTRATED 


NEW  YORK 

D.  VAN  NOSTRAND  COMPANY 

25  PARK  PLACE 

1910 


THE  AIR  PROPELLER 


BOOKS  BY  THE  AUTHOR 


On  Electricity 

The  Principles  of  the  Transformer 
Direct  and  Alternating  Current  Manual 

Experiments  with  Alternating  Currents  (being  Part 
II  of  Volume  II  of  A  Laboratory  Manual  of 
Physics,  edited  by  E.  L.  Nichols) 

Alternating  Currents:  an  Analytical  and  Graphical 
Treatment  for  Students  and  Engineers  (jointly 
with  A.  C.  Crehore) 

Also,  editions  in  French  and  German 

On  Aerodynamics 

Airplane  Characteristics,  1918;  cloth,  $1.60. 
The  Air  Propeller,  1919;  paper,  $1.00. 

The  Airplane,  in  preparation  for  1920;  cloth,  $3.00. 
Most  of  the  chapters  in  this  volume  will  consist 
of  material  to  be  published  therein  for  the  first 
time.  Six  chapters  will  consist  essentially  of 
material  that  has  appeared  in  the  two  preceding 
volumes,  revised  and  amplified. 

Orders  for  any  of  the  foregoing  works  may  be  sent 
to  D.  Van  Nostrand  Company,  25  Park  Place, 
New  York. 


THE  AIR   PROPELLER 

Its  working  characteristics  and  theory, 
together  with  a  brief  discussion  of  the 
airplane  engine  and  the  power  availa- 
ble for  airplane  propulsion 


BY 

FREDERICK  BEDELL,  PH.D. 

Professor  in  Physics,  Cornell  University 
Author  of  Airplane  Characteristics,  etc. 

Member  Aeronautical  Society  of  America,  Past  Vice-President 
American  Institute  of  Electrical  Engineers,  Fellow  and  Past 
General  Secretary  American  Association  for  the  Advancement 
of  Science,  Member  the  American  Physical  Society  and  Manag- 
ing Editor  of  The  Physical  Review. 


ILLUSTRATED 


NEW  YORK 

D.  VAN  NOSTRAND  COMPANY 

25  PARK  PLACE 

1919 


COPYRIGHT  1919 

BY 
FREDERICK  BEDELL 


Engineerisg 
Library 


PREFACE 

It  is  with  some  hesitation  that  the  writer  adds  to  the 
literature  of  the  propeller.  He  has  been  lead  to  do  so, 
however,  because  many  discussions  of  the  subject  are 
unsatisfying  and  in  some  cases  are  not  in  accord  with  fact. 
Indeed,  misconceptions  of  the  behavior  of  a  propeller  are  not 
uncommonly  held  even  by  those  who  are  otherwise  well- 
informed  on  aerodynamic  subjects. 

The  author  has  endeavored  to  present  a  brief  and  simple 
treatment  of  the  propeller  for  those  who  want  a  practical 
working  knowledge  of  its  characteristics  and  a  general 
knowledge  of  its  theory.  It  is  believed  that  the  treatment 
will  at  the  same  time  serve  as  a  general  introduction  for  those 
who  wish  to  pursue  the  subject  further  and  to  make  a  more 
detailed  study  of  the  propeller,  either  in  its  theoretical  or 
practical  aspects. 

As  the  material  herein  is  soon  to  be  revised  and  republished* 
in  another  form,  the  author  would  welcome  criticism,  and 
would  be  pleased  to  have  his  attention  called  to  any  error 
or  obscurity  in  presentation.  He  desires  to  thank  Professor 
S.  Noda,  Honorary  Fellow  in  Physics,  Cornell  University, 
for  valuable  assistance  in  the  preparation  of  this  book,  par- 
ticularly in  the  calculation  of  the  characteristics  of  the  pro- 
peller. 

ITHACA,  N.  Y., 
August,  1919. 


*To  be  included  in  The  Airplane,  now  in  preparation;    see  notice 
preceding  title  page. 


CONTENTS 

PAGE 

POWER  AVAILABLE  FROM  THE  AIR  PROPELLER  AND  THE 

AIRPLANE  ENGINE  -      9 

THE  AIRPLANE  ENGINE  n 

THE  AIR  PROPELLER 

(a)  Introductory  -     19 

(b)  Conditions  of  Propeller  Operation      -  25 

(c)  Propeller  Characteristics    -  31 

(d)  Propeller  Theory  67 

APPENDIX 

Glossary  -     77 

Power  Characteristics   (power  required)  -           91 


POWER  AVAILABLE  FROM  THE  AIR  PROPELLER 
AND  THE  AIRPLANE  ENGINE 

The  power  required  for  airplane  flight  at  different  veloci- 
ties depends  upon  airplane  structure,  varying  as  the  product 
of  airplane  velocity  and  the  total  airplane  resistance.  Neither 
the  source  of  power  nor  the  amount  of  power  available  is 
involved  in  the  determination  of  power  required,  which  is 
quite  independent  of  propeller  and  engine.  Curves  for  power 
required  are  shown  in  an  appendix  and  will  not  be  discussed 
here. 

On  the  other  hand,  the  power  that  is  available  for  driving 
the  airplane  forward,  called  power  available  or  thrust  horse 
power,  depends  entirely  upon  the  air  propeller  and  the  airplane 
engine.  The  power  available  is  derived  directly  from  the 
thrust  of  the  propeller,  being  proportional  to  the  product  of 
propeller  thrust  and  the  forward  velocity  of  the  airplane;  in 
horse  power,  it  is  equal  to  the  product  of  thrust  in  pounds  and 
velocity  in  miles  per  hour,  divided  by  375.  The  power 
necessary  for  driving  the  propeller  in  order  to  obtain  this 
thrust  is  supplied  by  the  airplane  engine.  Although  the 
propeller  and  engine  perform  their  separate  functions,  the 
conditions  of  operation  of  the  one  are  dependent  upon  the 
operating  characteristics  of  the  other,  for  the  power  the 
propeller  absorbs  must  exactly  equal  the  power  the  engine 
delivers  and  the  speed  of  rotation  of  the  one  must  be  the  speed 
of  rotation  of  the  other. 

Although  no  complete  discussion  of  the  airplane  engine 
can  be  here  undertaken,  an  outline  will  be  given  of  its  chief 
(9) 


10 


characteristics  that  have  a  bearing  on  the  power  available 
in  airplane  flight.  This  will  be  followed  by  a  more  complete 
discussion  of  the  air  propeller,  its  Conditions  of  Operation, 
its  Characteristics  and  its  Theory. 


11 

THE  AIRPLANE  ENGINE 

The  gas  engine  is  the  airplane  engine  in  general  use  on 
account  of  light  weight. 

The  internal  combustion  engine — or  the  "gas  engine"  as  it 
is  more  popularly  known — made  flight  possible ;  and,  although 
some*  of  its  characteristics  are  not  the  best  for  air- 
plane flight,  it  meets  the  important  requirement  of  low 
weight  per  horse  power.  Each  year  airplane  engines  have  been 
made  of  greater  power  and  less  weight  per  horse  power,  a 
great  advance f  being  made  by  the  Liberty  motor  (1918) 
which  gave  450  H. P.  with  a  weight  of  only  1.8  Ibs.  per  H.P. 

Although  other  types  of  engine  may  hereafter  be  intro- 
duced,— possibly  in  huge  aircraft  requiring  many  thousand 


*Particularly  undesirable  is  the  decrease  in  the  power  developed  by  a 
gas  engine  at  high  altitudes,  the  power  developed  being  in  direct  pro- 
portion to  the  density  of  the  air,  as  discussed  in  a  later  chapter.  At  an 
altitude  of  about  20,000  feet,  only  half  as  much  power  is  developed  as 
near  the  ground.  To  obviate  this  decrease  in  power  with  altitude 
has  been  the  aim  of  inventors.  Methods  for  accomplishing  this  have 
been  devised  but  are  not  in  general  use.  (The  chapter  on  altitude  is 
not  included  in  this  volume.) 

\Size  and  weight  of  engines. — The  original  motor  of  the  Wright 
Brothers,  used  in  the  first  airplane  flight  in  1903,  gave  12  horse  power, 
with  a  weight  of  12.7  Ibs.  per  horse  power.  The  development  of  the 
airplane  engine  since  then,  until  the  1918  Liberty  motor,  is  shown  by 
the  following  table.  The  numbers,  except  in  the'first  and  last  column, 
are  average  values  of  principal  engines  for  each  year. 

Year  1903  1910  1914  1915  1916  1917  1918 

Horsepower  12  54  112  133  185  243  450 

Weight,  Ibs.  152  309  437  512  570  693  825 

Lbs.perH.P.  12.7  5.7  3.9  3.8  3.1  2.8  1.8 

To  obtain  greater  power  than  can  be  obtained  from  a  single  engine, 
several  engines  (and  usually  as  many  propellers)  are  employed.  As 
many  as  six  engines,  developing  a  total  of  3000  H.  P.  have  thus  been 
used.  The  N  C  4  hydroplane,  in  the  first  trans-Atlantic  flight  (1919), 
was  equipped  with  four  Liberty  motors. 


12 


horse  power, — the  gas  engine  may  be  looked  upon  as  the 
standard  type  of  airplane  engine  and  it  only  need  be  here 
considered. 

Variation  of  engine  power  with  speed. 

The  power  developed  by  a  gas  engine,  with  throttle  wide 
open  or  in  other  constant  position,  increases  in  proportion 
to  the  number  of  explosions  in  a  given  time  and  hence  in 
proportion  to  the  number  of  revolutions  per  minute,  which 
hereafter  will  be  referred  to  as  the  speed  N.  For  a  consider- 
able range  of  speed  this  proportionality  is  quite  close,  power 
increasing  in  direct  proportion*  to  speed;  but  for  higher 
speeds  the  power  increases  less  rapidly,  and  finally  a  speed 
is  reached  at  which  the  power  is  a  maximum  and  beyond 
which  the  power  falls  off.  This  falling  off  in  power  is  due 
largely  to  the  fact  that  the  fuel-charge  received  in  the  cylin- 
ders for  each  explosion  is  reduced  at  high  speeds  on  account 
of  the  increased  friction  through  ports  and  passages. 

The  variation  of  power  with  speed  for  a  typical  enginef 
is  shown  in  Fig.  44,  in  which  the  solid  curve  shows  the  brake 
horse  power  when  the  throttle  is  wide  open.  It  is  seen  that 
power  increases  very  nearly  in  proportion  to  speed  until, 
in  this  case,  a  maximum  of  106  H.P.  is  reached  at  a  speed 
of  1240  R.  P.  M. 


*Power  varies  as  torque  x  speed.  When  power  varies  in  direct  pro- 
portion to  speed,  torque  is  constant.  The  torque  in  a  gas  engine  is 
nearly  constant  through  the  working  range.  As  the  power  curve  falls 
off  from  a  straight  line,  the  torque  decreases. 

fOne  hundred  H.  P.  Gnome  Monosoupape  Motor.  This  particular 
motor  is  no  longer  made.  Its  performance,  however,  may  be  taken  as 
typical. 


13 


120 

100 

80 

GO 
^-o 

20 


0         200         400       GOO        800        1000        1200       HOC 

SPEED,  REVOLUTIOMS  PER  MINUTE 


Fig.  44.  Variation  of  brake  horse  power  of  a  typical  gas 
engine  with  speed.  Dotted  curves  show  reduction  of 
power  by  throttle  control. 


15 

Mechanical  efficiency. 

The  entire  power  developed  by  the  explosions  in  the  cylin- 
ders of  a  gas  engine  is  called  the  indicated  horse  power  or 
I.  H.  P.  Some  of  this  power,  however,  is  wasted  in  friction 
and  other  losses  within  the  engine,  so  that  the  useful  delivered 
horse  power — called  the  brake  horse  power  or  B.  H.  P. — is, 
let  us  say,  10  or  15  per  cent,  less  than  the  indicated  horse 
power. 

The  mechanical  efficiency  of  the  engine  is  the  ratio  of  the 
brake  horse  power  to  the  indicated  horse  power;  thus 
when  the  losses  are  10  or  15  per  cent.,  the  mechanical  effi- 
ciency is  90  or  85  per  cent.  The  efficiency  of  an  engine, 
as  well  as  its  power,  varies  with  the  speed  at  which  the 
engine  is  run.  The  efficiency  is  low  at  low  speed  and  at  very 
high  speed  (*'.  e.,  when  the  power  delivered  is  low)  and  is 
nearly  a  maximum  when  power  is  a  maximum.  The  speed 
for  maximum  efficiency  is  a  little  lower  than  the  speed  for 
maximum  power,  but  the  efficiency  remains  high  (within  a 
few  per  cent,  of  its  maximum  value)  for  a  wide  range  of  speed 
— a  range,  let  us  say,  of  twenty  or  thirty  per  cent.  (In  Fig. 
44,  this  range  extends  roughly  from  the  beginning  of  the  word 
Throttle  to  the  point  of  maximum  power.) 

Range  of  engine  speed. 

The  best  speed  for  engine  operation  is  no  one  precise 
speed  but  extends  through  a  moderate  range  of  values  just 
below  the  speed  for  maximum  power.  In  this  range,  effi- 
ciency and  power  are  both  high ;  beyond  this  range,  however, 
there  is  a  large  falling  off  both  in  efficiency  and  in  power. 

An  engine  is  often  run  at  a  lower  speed  than  this  best 
range,  when  such  lower  speed  and  power  is  desirable,  despite 
the  lower  efficiency;  but  it  is  rarely  run  at  much  higher 


16 

speed,  on  account  of  increased  wear  and  heating  of  the  engine, 
as  well  as  decrease  in  power  and  efficiency. 

The  best  speed  depends  upon  the  design  of  the  engine, — 
size  of  ports  and  bore,  length  of  stroke,  mass  of  moving  parts, 
etc.  As  a  usual  thing,  airplane  engines  are  designed  for  a 
lower  speed  than  automobile  engines  so  as  to  permit  of 
direct  connection  to  the  propeller.  Structural  and  other 
reasons  make  high  propeller  speeds  undesirable,  the  usual 
speeds  being  between  1200  and  1600  R.  P.  M.;  but  speeds 
beyond  this  range  are  not  uncommon. 

A  propeller  may  be  geared  down,  so  as  to  gain  the  advan- 
tage of  high  engine  speed  with  low  propeller  speed,  but 
this  gearing  adds  weight,  introduces  losses  and  is  an  added 
source  of  trouble. 

Throttle  control. 

The  solid  curve  for  brake  horse  power  in  Fig.  44  shows 
the  full  power  when  all  adjustments  of  throttle,  spark  and 
carburetor  are  made  so  as  to  give  the  greatest  possible  power 
at  each  speed.  Usually,  the  pilot  controls  the  power  by 
means  of  the  throttle,  less  power  being  obtained  by  partly 
closing  the  throttle.  (In  some  engines,  however,  the  only 
power  control  is  the  ignition  switch,  by  which  the  power 
is  turned  either  entirely  on  or  off.) 

Dotted  curves  in  the  same  figure,  marked  "three-quarters 
throttle"  and  "half  throttle,"  show  the  power  obtained  by 
throttling  the  engine  so  that,  at  each  speed,  the  power  is 
three-quarters  or  one-half  the  full  power  at  that  speed. 
To  obtain  precisely  the  same  fraction  of  full  power  at  each 
speed  would  require  some  adjustment  of  throttle  (with 
constant  throttle,  the  fractional  power  being  not  exactly 
three-fourths  or  one-half,  or  other  definite  proportion  of 


17 


full  power,  at  all  speeds),  but  this  adjustment  would  not  be 
great.  The  curves  may,  therefore,  be  considered  as  illustrat- 
ing the  variation  of  power  with  speed  for  various  constant 
throttle  positions;  they  are  sufficiently  correct  for  this  pur- 
pose, although  for  exact  computation  they  would  require 
some  modification.  (These  dotted  curves  practically  show, 
also,  the  decreased  power  at  higher  altitudes,  for,  as  discussed 
later  under  Altitude,  the  decrease  in  air  density  causes  a 
decrease  in  power  substantially  the  same  as  throttling.) 

The  curves  in  Fig.  44  are  engine  characteristics  and  show 
the  power  delivered  by  the  engine  at  different  speeds  and 
with  different  amounts  of  throttle.  Before  we  can 
determine  how  much  power  is  available  for  flight,  we  must 
examine  the  characteristics  of  the  air  propeller. 


19 


THE  AIR  PROPELLER 
(a)     Introductory 

The  air  propeller  is  mounted  on  or  geared  to  the  engine 
shaft,  —  either  ahead  of  the  engine  as  a  tractor,  or  behind  it 
as  a  pusher.  The  propeller  is  usually  constructed  with  two 
blades;'  as  in  Fig.  45^  but  not  uncommonly  it  is  constructed 
with  four  and  less  commonly  with  three  blades  when  propel- 
ler diameter  is  limited  by  the  space  available.  The  three- 
blade  propeller  is  structurally  difficult.  The  requisite 
strength  is  most  readily  obtained  with  two  blades,  which 
pass  through  the  hub  as  one  member. 

The  forward  thrust  required  to  overcome  airplane  resist- 
ance in  flight  is  obtained  by  the  propeller  driving  back  a 
stream  of  air  in  a  so-called  slip-stream;  the  greater  the 
backward  velocity  of  this  slip-stream  and  the  greater  its 
volume,  the  greater  is  the  forward  reaction  or  propeller 
thrust. 

In  the  same  way  that  an  upward  force  or  lift  is  obtained 
from  a  moving  aerofoil  because  it  deflects  the  air  stream 
downward,  a  forward  force  or  thrust  is  obtained  from  a  moving 
propeller  blade  because  it  drives  the  air  stream  backward. 
In  each  case  the  force  is  a  reaction  obtained  by  deflecting  or 
driving  the  air  particles  in  a  direction  opposite  to  the  force. 

Although  there  are  various  ways  of  treating  the  propeller 
and  it  is  commonly  referred  to  and  considered  as  an  air  screw, 
it  is  most  satisfactory  to  consider  the  propeller  blade  —  or 
each  element  thereof  —  as  an  aerofoil,  with  lift  and  drag 
determined  by  its  cross-section  and  angle  of  incidence  as 
for  any  aerofoil.  The  lift  of  a  propeller  blade  as  an  aerofoil 
determines  its  thrust  as  a  propeller;  its  drag  as  an  aerofoil 
determines  the  torque  necessary  to  drive  it  as  a  propeller,  ] 
as  discussed  more  fully  later. 


20 

\  Screw  definitions;  pitch  and  pitch  ratio. 

Although  the  action  of  a  propeller  is  very  different  from 
that  of  a  screw,  various  terms  that  originated  with  the  screw 
are  applied  to  the  propeller. 

When  a  screw  passes  through  a  solid,  the  distance  it  moves 
forward  in  one  revolution  is  called  the  pitch  of  the  screw. 
This  distance  divided  by  the  diameter  of  the  screw  is  called 
its  pitch  ratio.  The  pitch  and  pitch  ratio  of  a  screw  may 
be  exactly  determined  from  its  dimensions  (the  distance 
between  threads,  and  the  diameter),  the  values  thus  deter- 
mined being  identical  with  the  values  determined  by  actually 
driving  the  screw  through  a  solid  or  turning  a  bolt  in  a  nut. 

The  terms  pitch  and  pitch  ratio  are  applied  to  a  propeller 
as  to  a  screw.  It  is  found,  however,  that  the  effective  pitch* 
of  a  propeller  —  the  distance  the  propeller  moves  forward 
through  the  air  in  one  revolution  —  is  not  the  same  as  its 
structural  pitch  (also  called  nominal  pitch  or  geometrical 
pitch)  determined  from  its  dimensions  as  a  screw  passing 
through  a  solid. 

In  propeller  operation  it  is  its  effective  pitch,  rather  than 
its  structural  pitch,  in  which  we  are  most  interested.  (As 
shown  later,!  the  effective  pitch  of  a  propeller  varies  with 
conditions  of  operation,  being  sometimes  less  and  sometimes 
more  than  the  structural  pitch  which  has  but  one  value  fixed 
by  its  dimensions. 

I  *"~ 
Definitions  of  torque  horse  power,  thrust  horse  power  and 


The  power  availabls  for  propelling  an  airplane  through  the 
air  comes  directly  from  the  propeller  thrust,  the  amount 


"Called  also  "experimental  pitch." 


21 


Fig.  45.     Two-blade  propeller. 


23 

of  power  thus  furnished,  as  already  pointed  out,  being  pro- 
portional to  the  product  of  propeller  thrust  and  airplane 
velocity.  The  propeller  itself,  however,  does  not  create 
this  power;  it  merely  transmits  power  that  it  receives  from 
the  engine,  the  power  it  thus  receives  being  proportional  to 
the  product  of  the  torque*  in  the  propeller  shaft  and  its  speed 
in  revolutions  per  minute.  The  speed  of  the  propeller  is 
the  speed  of  the  engine,  unless  reduced  by  gearing.  "Speed," 
here  and  elsewhere  in  this  discussion,  refers  to  speed  of  rota- 
tion, often  referred  to  as  "revs."  or  R.  P.  M.,  and  not  to  the 
forward  translation  referred  to  as  "velocity"  or  "miles  per 
hour." 

Of  the  three  elements  for  flight, — engine,  propeller  and 
airplane, — the  propeller  is  thus  seen  to  be  the  intermediary 
or  "middle-man,"  receiving  power  from  the  engine  and 
delivering  this  power  in  a  form  available  for  propelling  the 
airplane.  The  power  the  propeller  receives  is  torque 
horse  power  and  this  is  the  brakehorse  power  of  the  engine 
("already  discussed/)  The  power  the  propeller  delivers  is 
thrust  horse  power  and  this  is  the  power  available  for  air- 
plane propulsion. 

The  efficiency  of  a  propeller  is  the  ratio  of  thrust  horse 
power  to  torque  horse  power.  The  entire  output  of  the  engine 
would  thus  be  available  as  thrust  horse  power  for  propelling 
the  airplane,  if  the  efficiency  of  the  propeller  were  100  per 
cent.  On  account  of  losses,  however,  the  efficiency  of  a 
propeller  is  less  than  100  per  cent.,  so  that  not  all  of  the 
engine  output  is  thus  available.  Under  best  conditions, 


*Torque  is  a  turning  moment  equal  to  the  product  Fr  of  a  force  F  and 
the  perpendicular  distance  r  from  the  force  to  the  center  of  rotation. 
If  F  is  in  pounds  and  r  in  feet,  torque  horse  power  is  2  v  N  F  r/33OOO, 
for  one  horse  power  is  33000  ft.  Ibs.  per  min. 


24 

the  efficiency  of  a  propeller  may  be  80  or  85  per  cent.,  but 
under  working  conditions  it  is  usually  less;  thus,  when  the 
brake  horse  power  of  the  engine  is  100,  perhaps  only  60  or  70 
horse  power  may  be  available  for  propeller  thrust. 

The  air  propeller,  working  in  a  compressible  medium,  is 
more  efficient  than  the  marine  propeller  working  in  a  medium 
that  is  practically  incompressible.  The  rarefaction  and  com- 
pression before  and  behind  the  blade  of  a  propeller  in  air — 
as  above  and  below  an  aerofoil — are  factors  not  found  in 
water.  (In  water,  when  a  negative  pressure  created  by 
the  relative  motion  of  blade  and  water  exceeds  the  static 
pressure  of  the  water,  it  is  not  possible  for  the  water  to  become 
rarefied  but  a  discontinuous  flow  occurs  known  as  cavitation. 
To  avoid  this,  the  blades  of  a  marine  propeller  are  made 
short  and  wide,  and  not  long  and  narrow  as  in  an  air  propel- 
ler.) 

A  knowledge  of  how  power*  and  efficiency  are  affected  by 
different  conditions  of  operation  is  most  essential  for  the 
understanding  of  the  propeller.  Fortunately  these  relations, 
so  far  as  results  in  operation  are  concerned  are  simple. 

Let  us  first  see  what  are  the  varying  conditions  of  propeller 
operation.  We  will  then  see  what  are  the  characteristics 
of  a  propeller  under  these  different  conditions  of  operation, 
after  which  we  will  consider  the  theory  of  the  propeller  that 
accounts  for  these  characteristics. 


*Power  is  of  first  importance.  It  makes  little  difference  how  efficient 
a  propeller  is,  if  it  does  not  have  enough  power  to  do  its  intended  work. 
A  small  desk  fan,  even  were  it  100  per  cent,  efficient,  would  not  serve 
for  propelling  an  airplane  so  well  as  a  propeller  with  adequate  power 
having  an  efficiency  of  only  50  per  cent.  Adequate  power  being  assured, 
conditions  of  operation  that  give  high  efficiency  should  be  sought. 


25 

(6)     Conditions  of  Propeller  Operation 
V  and  N,  the  two  variables  in  propeller  operation. 

During  flight  the  two  variables  in  propeller  operation 
upon  which  other  quantities  depend  are  its  forward  velocity 
V  and  its  speed  or  revolutions  per  minute  N.  (The  effect 
of  a  third  variable,  the  change  of  air  density  with  altitude,  is 
left  for  a  later  discussion.)  The  dimensions  and  shape  of 
the  propeller  itself  can  only  be  changed  by  a  change  of  pro- 
peller when  not  in  flight.* 

It  will  be  found  that  propeller  characteristics  depend  not 
only  upon  the  absolute  values  of  V  and  N  but  upon  their 
relative  values  as  well.  The  ratio  of  V  to  N,  and  the  ratio 
V  /ND,  where  D  is  propeller  diameter,  have  special  significance. 

The  values  of  V  and  N  are  known  to  the  pilot  by  his  air- 
speed meter  and  his  revolution  indicator.  They  are,  further- 
more, quantities  that  he  directly  controls.  For  these  rea- 
sons, propeller  characteristics  are  better  understood — by  a 
pilot  at  least — when  expressed  in  terms  of  V  and  N  than 
when  expressed  in  terms  of  effective  pitch,  angle  of  blade 
incidence  or  slip,  quantities  that  are  only  indirectly  known 
and  controlled  by  the  pilot.  It  is  well,  however,  to  be  able  to 
interpret  propeller  characteristics  when  expressed  in  these 
various  terms,  for  each  has  its  significance;  effective  pitch 
and  slip  are  convenient  terms  in  the  comparison  of  propellers 
of  different  diameter,  while  the  angle  of  incidence  the  blade 
makes  with  the  air  is  useful  in  propeller  theory,  as  discussed 
later. 


*Adjustable  propellers,  in  which  the  pitch  can  be  changed  during 
flight,  have  been  used  but  have  not  been  widely  introduced. 


26 

V/N,  the  forward  travel  per  revolution  or  effective  pitch. 

When  a  propeller  making  N  revolutions  per  minute,  is 
moving  forward  with  a  velocity  of  V  ft.  per  minute,  the 
distance  that  the  propeller  moves  forward  in  one  revolution 
is  seen  to  be  V/N  feet.  This  distance,  in  feet  or  other  unit 
of  length,  is  called  the  effective  pitch  of  the  propeller;  it 
varies  with  the  relative  values  of  V  and  N,  under  different 
conditions  of  operation,  but  is  independent  of  their  absolute 
values.  (Thus,  when  V  =  5000  ft.  per  min.  and  N  =  1000 
R.  P.  M.,  the  propeller  moves  forward  in  one  revolution 
a  distance  V/N  =  5  ft.,  which  is  the  effective  pitch  of  the 
propeller;  when  V  =  6000  and  N  =  1200,  the  effective  pitch 
V/N  is  still  equal  to  5  ft.) 

V/ND,  the  ratio  of  forward  travel  per  revolution  to  diameter, 
or  effective  pitch  ratio. 

This  forward  travel  per  revolution,  when  expressed  in 
term  of  propeller  diameter  D  (instead  of  in  feet)  is  V/ND  and 
is  called  the  effective  pitch  ratio.  Thus,  in  the  preceding 
example,  if  the  propeller  has  a  diameter  of  8  feet,  V/ND  = 
5  -f-  8  =  0.625,  which  is  the  effective  pitch  ratio  of  the  pro- 
peller and  means  that  in  each  revolution  the  propeller  travels 
forward  a  distance  0.625  times  its  diameter.  V/ND  is  a 
number,  independent  of  units ;  the  units  used,  however,  must 
be  consistent.* 


*If  N  is  expressed  in  R.  P.  M.  and  D  in  feet,  V  must  be  expressed  in 
ft.  per  minute.  For  example,  an  8  ft.  propeller  makes  1200  R.  P.  M. 
When  V/ND  =  0.5,  V  =  0.5  X  1200  X  8  =  4800  ft.  per  min.  (54.5 
MPH.);  when  V/ND  =  i,  V  =  9600  ft.  per  min.  (109  MPH.).  The 
value  of  V/ND  is  frequently  in  this  range  (0.5  to  i.o),  but  these  values 
are  given  for  illustration  and  not  as  limits. 

If  N  were  revolutions  per  sec.  and  D  meters,  V  must  be  meters  per 
second;  V/ND  would  be  unchanged,  being  independent  of  units. 


27 

The  value  of  V  /ND  indicates,  to  a  certain  extent,  the 
conditions  of  propeller  operation.  Being  independent  of 
units,  it  is  more  useful  for  this  purpose  than  V  /N.  Various 
propeller  quantities  (for  example,  efficiency,  Figs.  55  and  56) 
are  accordingly  plotted  in  terms  of  V/ND. 

Since  the  peripheral  velocity  of  a  propeller  is  nND,  it  is 
seen  that  V/ND  is  proportional  to  the  ratio  of  the  forward 
velocity  to  the  peripheral  velocity  of  the  propeller  tip. 

Dynamic  pitch  and  pitch  ratio. 

The  effective  pitch,  or  forward  travel  of  a  propeller  per 
revolution,  as  ju.st  stated  varies  under  different  conditions  of 
operation.  It  will  be  shown  later,  that  as  effective  pitch 
increases,  thrust  decreases  and  finally  becomes  zero.  The 
propeller  then  goes  through  the  air  smoothly,  as  a  screw  with 
no  slip,  without  disturbing  the  air  and  without  imparting 
velocity  to  the  air  particles. 

The  particular  value  of  effective  pitch  that  gives  zero 
thrust  is  called  the  dynamic  pitch  of  the  propeller.  It  is 
characteristic  of  each  propeller  and  like  a  dimension  (ex- 
pressed in  feet  or  other  unit  of  length)  can  not  be  changed. 

The  dynamic  pitch  ratio  is  the  ratio  of  the  dynamic  pitch 
to  the  propeller  diameter  D,  and  is  a  number  independent  of 
units.  Otherwise  defined,  it  is  the  value  of  V/ND  when 
there  is  no  thrust  and  no  slip. 

As  an  illustration,  if  a  10  ft.  propeller  creates  no  thrust 
when  its  forward  travel  per  revolution  is  V /N  =  9  ft.,  the 
dynamic  pitch  ratio  is  V/ND  =  9-5-10  =  0.9.  This  is 
a  constant  of  the  propeller  and  is  the  same  whether  V  and  N 
be  large  or  small.  Practical  values  for  dynamic  pitch  ratio 
are  between  0.5  and  1.5. 


28 

Slip. 

Positive  thrust  is  obtained  only  when  the  forward  travel 
per  revolution,  or  the  effective  pitch,  is  less*  than  the  dynamic 
pitch.  The  difference  between  the  dynamic  pitch  and  the 
effective  pitch,  expressed  as  a  percentage  of  the  former,  is 
called  the  slip.  Thus,  when  a  propeller  with  a  dynamic  pitch 
of  8  feet  travels  forward  only  6  feet  in  one  revolution,  the  slip 
is  25  per  cent.,  or  0.25. 

When  the  slip  is  5  per  cent.,  the  forward  travel  per  revolu- 
tion is 

V  JN  =  effective  pitch  =  (i  — s)  dynamic  pitch. 
As  a  ratio  in  terms  of  D,  we  have  accordingly 
V/ND  =  effective  pitch  ratio 
=  (i  —  s)  dynamic  pitch  ratio. 

It  is  seen  that  when  the  slip  is  zero,  the  effective  pitch 
becomes  equal  to  the  dynamic  pitch. 

Dynamic  pitch  greater  than  structural  pitch. 

The  dynamic  pitch  and  pitch  ratio  of  a  propeller  is  greaterf 
than  the  nominal  or  structural  pitch  and  pitch  ratio.  In 
other  words^  the  actual  forward  travel  of  a  propeller  through 
the  air  for  no  thrust  is  greater  than  its  travel  calculated  as  a 
screw  passing  through  a  solid,  unyielding  material.  It  is  for 
this  reason  that  the  screw  theory  of  the  propeller  is  abandoned. 

The  explanation  lies  in  the  fact  that  the  air  through  which 
the  propeller  is  passing  is  a  compressible  gas  and  not  an 
unyielding  solid.  The  propeller  blade  in  cutting  through  the 
air  acts  not  as  a  screw  but  as  an  aerofoil — as  discussed  later 


*When  the  travel  is  greater  than  the  dynamic  pitch  and  the  slip  is 
negative  (as  in  diving)  a  negative  thrust  is  developed,  the  propeller 
then  acting  as  a  brake;  see  Fig.  51. 

fForty-eiglrt  propellers  discussed  by  Durand  in  Report  No.  14, 
referred  to  later,  have  values  of  dynamic  pitch  between  1.17  and  1.54 
times  the  nominal  pitch. 


29 

under  propeller  theory — and,  like  any  aerofoil,  gives  rise  to  a 
rarefaction*  on  its  upper  surface  (in  front  of  the  propeller) 
and  a  condensation  on  the  lower  surface  (back  of  propeller) . 
Calculations  for  a  propeller  as  a  screw  take  no  account  of  this 
rarefaction  and  condensation  of  the  air  and  for  this  reason 
calculated  or  nominal  values  for  pitch  and  pitch  ratio  always 
differ  from  the  actual  dynamic  values.  The  result  in  flight  is 
much  the  same  as  though  the  whole  body  of  air  immediately 
surrounding  a  propeller  were  being  carried  forward  with  it, 
so  that  more  than  the  calculated  velocity  is  necessary  in 
order  to  get  zero  thrust  and  this  may  serve  as  a  rough  ex- 
planation. 

Dynamic  pitch  and  pitch  ratio  can  only  be  determined  by 
experiment,  where  special  facilities  are  available,  whereas 
nominal  pitch  or  structural  pitch  and  pitch  ratio  can  be 
determined  by  measurements  described  later  on  the  propeller 
itself.  For  this  reason  the  values  for  pitch  and  pitch  ratio 
usually  given  are  nominal  values,  and  are  always  so  under- 
stood unless  otherwise  specified, 

The  relation  between  V  and  N  and  the  significance  of  slip, 
pitch  and  pitch  ratio  in  propeller  operation  will  be  brought 
out  more  fully  in  the  subsequent  discussion  of  propeller 
characteristics  and  propeller  theory. 


*See  "Airplane  Characteristics,"  p.  117. 


31 


(c)     Propeller  Characteristics 

The  behavior  of  a  propeller  under  various  conditions  of 
operation  will  be  understood  by  examining  the  characteristic 
curves  that  follow.  These  are  working  results,  independent 
of  any  theory,  the  performance  of  the  propeller  being  to 
many  readers  of  first  importance.  A  discussion  of  theory 
will  follow,  but  some  may  prefer  to  read  the  theory  before 
examining  the  performance. 

The  conditions  of  operation  depend  upon  the  relation 
between  V  and  N,  and  this  in  turn  requires  first  a  study  of 
torque  horse  power.  Other  characteristics  will  be  studied  in 
turn. 

Torque  horse  power  for  different  values  of  N  and  V. 

The  torque  horse  power  required  to  drive  a  given  propeller 
varies  both  with  its  speed  N  (revolutions  per  minute)  and  the 
forward  velocity  V  (miles  per  hour)  at  which  it  is  moving 
through  the  air. 

For  any  constant  value  of  V,  torque  horse  power  increases 
as  the  revolutions  per  minute  increase;  in  other  words,  it  is 
found,  as  might  be  supposed,  that  more  power  is  required  to 
turn  a  propeller  fast  than  to  turn  it  slowly.  This  is  shown 
by  the  curves  in  Fig.  46  for  the  torque  horse  power  of  a 
particular*  propeller  at  three  different  velocities,  50,  100  and 
150  miles  per  hour. 

By  comparing  these  curves  it  is  seen  that  the  torque  horse 
power  is  less  for  high  than  for  low  velocities. 


"The  curves  in  Figs.  46  (and  subsequent  curves,  unless  otherwise 
stated)  relate  to  a  propeller  8'  9"  in  diameter,  with  nominal  pitch  ratio  0.9. 
The  curves  have  been  plotted  from  calculations  based  upon  experimental 
data  for  Propeller  No.  3,  as  given  by  W.  F.  Durand  in  Report  No.  14, 
National  Advisory  Committee  for  Aeronautics,  1917.  All  curves 
relate  to  ground  level,  air  density  =  0.0789.  The  point  m  on  any  curve 
is  the  point  of  maximum  propeller  efficiency. 


32 


The  decrease  in  torque  horse  power  as  V  increases  is  better 
shown  by  the  curves  in  Fig.  47  in  which  N  is  constant  and  V 
is  variable.  It  takes  less  power  to  drive  a  propeller,  at  any 
given  number  of  revolutions  per  minute,  when  the  propeller 
has  a  forward  velocity  V  than  when  it  is  stationary.  Pro- 
peller thrust,  as  discussed  later,  is  a  maximum  when  the 
propeller  is  stationary;  torque,  also,  is  then  a  maximum,  as 
well  as  torque  horse  power  as  shown  by  the  curves. 

As  V  increases,  torque  horse  power  continues  to  decrease 
and  becomes  zero  when  a  certain  velocity  is  reached.  At 
higher  velocities,  torque  horse  power  is  negative;  the  pro- 
peller, instead  of  receiving  power  from  the  engine,  then  drives 
the  engine,  receiving  power  as  an  air  motor  from  the  air. 
This  means  that  the  airplane  is  descending  in  a  glide  or  dive 
and  that  power  is  supplied  by  gravity.  The  airplane  is 
being  retarded  by  the  propeller  as  by  a  brake. 

Torque  horse  power  is  an  important  element  in  determin- 
ing the  relation  between  N  and  V. 

Relation  between  N  and  V. 

The  velocity  V  of  an  airplane  in  flight  is  determined  by 
its  angle  of  incidence,  as  discussed  in  Chapter*  II,  and  is 
controlled  entirely  by  the  elevator.  The  revolutions  per 
minute  or  speed  N,  although  controlled  by  the  throttle, 
depend  not  only  upon  engine  throttle  but  also  upon  airplane 
velocity  V.  Let  us  see  in  what  way  the  speed  N  is  determined. 

For  any  given  velocity,  for  example  V  =  100  M  P  H.,  we 
have  a  curve,  as  in  Fig.  46,  showing  torque  horse  power  for 
each  value  of  speed  N.  But  torque  horse  power  received  by 
the  propeller  must  equal  brake  horse  power  delivered  by  the 
engine.  The  engine  and  propeller,  accordingly,  speed  up 


*See  "Airplane  Characteristics." 


33 


until  a  speed  N  is  reached  at  which  the  propeller  absorbs 
all  the  power  output  of  the  engine,  that  is,  they  speed  up 
until  torque  horse  power  of  the  propeller  and  brake  horse 
power  of  the  engine  are  exactly  equal. 

This  is  made  clear  in  Fig.  48,  which  shows  a  curve  for 
engine  brake  horse  power  for  a  particular  amount  of  throttle 
(reproduced  from  Fig.  44  with  full  throttle)  and  a  curve  for 
propeller  torque  horse  power  for  a  particular  velocity 
(reproduced  from  Fig.  46  for  V  =  100  M  P  H.)  The  inter- 
section* of  these  two  curves  determines  the  speed  N  and  also 
the  power,  for  the  particular  value  of  V  and  particular  amount 
of  throttle.  The  intersection  will  be  shifted  as  either  curve 
is  shifted  by  control  of  throttle  or  change  of  V;  or,  both 
curves  may  be  shifted  simultaneously  with  a  sort  of  scissors 
motion. 

Value  of  N  for  different  amounts  of  throttle. — The  control  of 
speed  and  power  by -throttle,  for  one  value  of  V,  is  shown  in 
Fig.  49.  As  the  throttle  is  changed  from  "full  throttle"  to 
"24  throttle"  and  "J^  throttle,"  the  intersection  is  changed 
from  N'  to  N"  and  N"',  with  corresponding  change  in  speed 
and  power. 

Value  of  N  for  different  values  of  V. — The  change  of  speed 
and  power  for  several  different  values  of  V,  is  shown  in  the 
same  manner  in  Fig.  50.  The  speed  and  power  corresponding 
to  velocities  of  50,  75,  100,  125  and  150  M  P  H.,  are  deter- 
mined for  "full  throttle,"  "K  throttle"  or  "tf  throttle," 
by  the  several  intersections. 

*Curves  may  be  drawn  for  engine  and  propeller  torque,  instead  of 
engine  and  propeller  power,  determining  N  by  their  intersection  in  the 
same  manner.  Curves  for  propeller  torque,  at  different  speeds  N,  are 
continuously  rising  curves,  somewhat  like  the  curves  for  torque  horse 
power  in  Fig.  46.  Curves  for  engine  torque  at  different  speeds  are 
nearly  horizontal,  through  a  certain  range  of  speed,  dropping  sharply  at 
higher  speeds.  * 


34 

It  is  seen  that  the  speed  N  of  engine  and  propeller  depends 
not  only  upon  engine  throttle  (which  is  directly  controlled  by 
the  pilot),  but  also  upon  airplane  velocity,  which  is  indirectly 
controlled  by  the  pilot  by  means  of  the  elevator.  For 
constant  throttle,  there  is  a  definite  speed  N  corresponding 
to  each  velocity  V;  and  for  constant  velocity,  there  is  a 
definite  speed  N  for  each  position  of  the  throttle. 

The  curves  shown,  Figs.  48,  49  and  50,  relate  to  a  particular 
propeller  and  engine;  for  other  engines  and  propellers  the 
general  nature  of  the  results  would  be  the  same,  although 
numerical  results  would  differ. 

Thrust  horse  power  at  varying  velocities. 

A  consideration  of  the  thrust  horse  power  delivered  by  a 
propeller  under  different  conditions  of  operation  is  obviously 
of  utmost  importance,  the  sole  purpose  of  a  propeller  being  to 
produce  thrust  and  thrust  power.  Like  other  propeller 
quantities  these  both  vary  as  N  and  V  are  varied.  It  is, 
however,  most  satisfactory  to  plot  their  values  for  varying 
values  of  V,  so  that  direct  comparison  can  be  made  between 
curves  for  thrust  power  (power  available)  and  curves  for 
airplane  power  required,  which  are  plotted  in  terms  of  V. 

Before  discussing  thrust  power,  let  us  consider  propeller 
thrust  upon  which  thrust  power  depends. 

Propeller  thrust. — Thrust  depends  upon  the  backward 
velocity  imparted  to  the  air  by  the  propeller,  that  is,  the 
backward  velocity  of  the  slip  stream  with  respect  to  the 
surrounding  stationary  air.  The  thrust  developed  by  a 
propeller  will,  accordingly,  vary  with  the  forward  velocity  V 
of  the  propeller  and  will  be  a  maximum  when  V  is  zero,  namely, 
when  the  airplane  is  stationary),  for  the  velocity  of  the  slip 


35 


stream,  with  respect  to  the  surrounding  air,  is  then  a  maxi- 
mum. The  thrust,  when  the  airplane  is  stationary,  is  called 
the  static  thrust. 

When  the  propeller  is  moving  forward  with  a  velocity  V, 
the  backward  velocity  of  the  slip  stream  (which  remains 
unchanged  with  respect  to  the  propeller)  is  less  with  respect 
to  the  surrounding  stationary  air  and  the  thrust  is  accordingly 
less.  Thrust  decreases  as  V  increases,  as  shown  in  Fig.  51. 

Thrust  continues  to  decrease  as  V  increases,  and  finally 
thrust  becomes  zero  when  the  propeller  has  a  forward  velocity 
V  just  equal  to  the  backward  velocity  of  the  slip  stream 
relative  to  the  propeller.  The  velocity  of  the  slip  stream, 
with  respect  to  the  stationary  air,  is  then  zero  and  no  thrust 
is  created,  for  no  velocity  has  been  imparted  to  the  air  by 
the  propeller.  Slip  is  then  zero. 

The  solid  curve  in  Fig.  51  shows  the  variation  of  thrust 
with  velocity  for  a  particular  propeller  when  driven  at  1200 
R.P.M.  The  dotted  curves  show  the  thrust  at  1000  and  800 
R.P.M.  In  all  cases  zero  slip  corresponds  to  zero  thrust; 
100  per  cent,  slip  corresponds  to  zero  velocity. 

Thrust  horse  power  derived  from  thrust. — Thrust  horse  power 
is  readily  derived  from  thrust,  being  equal  to  the  product 
of  thrust  and  velocity,  divided  by  3  7  5  when  thrust  is  in  pounds 
and  velocity  is  in  miles  per  hour. 

Fig.  52  shows  curves  for  thrust  and  velocity,  and  a  curve 
for  thrust  power  thus  obtained  from  their  product.  It  is 
seen  that  thrust  power  is  zero  when  V  =  o,  at  100  per  cent, 
slip;  thrust  is  then  a  maximum.  It  is  seen,  also,  that 
thrust  power  is  zero  when  thrust  is  zero,  at  zero  slip ;  V  then 
has  a  certain  definite  value.  These  curves  are  drawn  for  a 
constant  speed,  N  =  1200  R.P.M. 


A  curve  for  torque  horse  power,  reproduced  from  Fig.  47, 
is  shown  in  Fig.  52  for  comparison;  this  makes  possible  a 
determination  of  efficiency,  discussed  later. 

For  the  case  shown  in  Fig.  52,  maximum  thrust  .power  is 
obtained  when  the  slip  is  44  per  cent. ;  maximum  efficiency, 
at  the  point  m,  when  the  slip  is  28.7  per  cent. 

Thrust  horse  power  for  different  values  of  speed  N. 

The  curves  in  Fig.  53  show  the  variation  of  thrust  horse 
power  with  velocity  for  a  propeller  driven  at  different  speeds 
N.  They  strikingly  show  that,  for  each  speed,  there  is  a 
certain  velocity  at  which  the  power  is  a  maximum,  and  that 
the  value  of  this  maximum  is  greater  for  greater  values  of 
speed  N. 

These  are  the  so-called  curves  for  power  available  which 
— when  compared  with  the  curves  for  power  required — 
have  an  important  bearing  upon  power  relations  in  flight. 
They  are  the  most  useful  of  propeller  curves  and  should  be 
carefully  studied  so  that  a  picture  of  them  may  be  kept  in 
mind.  Although  plotted  for  a  particular  propeller,  they  are 
typical  of  the  curves  for  power  available  for  any  propeller. 
They  are  independent  of  the  motor  used,  for  any  motor  (not 
necessarily  a  gas  engine)  may  be  used  provided  it  has  suffi- 
cient power  to  drive  the  propeller.  (Curves  for  propeller 
thrust  horse  power,  when  a  particular  engine  is  used,  are 
shown  later  in  Fig.  57.) 

A  propeller  delivers  its  maximum  power  when  the  slip  is, 
say,  40  to  50  per  cent,  (in  this  case  about  45  per  cent.); 
it  has  its  maximum  efficiency  — discussed  in  a  later  paragraph 
— when  the  slip  is,  say,  25  to  40  per  cent,  (in  this  case  about 
30  per  cent.) .  There  is  considerable  variation  in  these  values 
with  different  propellers,  but  maximum  power  always  occurs 


37 


at  a  greater  slip  than  maximum  efficiency.  The  best  range 
for  propeller  operation  is  between  the  point  for  maximum  power 
and  the  point  for  maximum  efficiency. 

Thrust  horse  power  for  propellers  of  different  diameters  D. 

Greater  thrust  horse  power  can  be  obtained  by  increasing 
N  as  just  shown,  but  is  often  better  obtained  by  using  a 
propeller  of  larger  diameter  D,  the  greater  power  in  this 
case  being  due  to  the  greater  volume  of  the  air  stream. 
The  curves  in  Fig.  54  show  the  power  obtained,  at  different 
velocities,  from  propellers  of  different  diameters. 

An  airplane  should  be  designed  for  as  large  a  propeller  as 
space  permits,  for  a  large  propeller  at  moderate  speed  is 
(generally  speaking)  better  than  a  smaller  propeller  at  very 
high  speed;  but  the  larger  propeller  is  objectionable  if  it 
necessitates  an  undue  elevation  of  the  center  of  gravity  of  the 
airplane.  On  account  of  this  limitation  and  the  necessity 
of  having  sufficient  clearance  between  the  propeller  and  the 
ground,  the  huge  propellers  satisfactorily  used  on  airships 
are  not  used  on  airplanes.  A  clearance  as  little  as  10  inches 
has  been  found  sufficient  in  some  types  of  planes. 

Assured  of  sufficient  thrust  power  delivered  by  the  propel- 
ler, we  next  inquire  as  to  the  efficiency  of  the  propeller  under 
different  conditions  of  operation. 

Propeller  efficiency  for  different  values  of  V/ND. 

The  efficiency  of  a  propeller  is  equal  to  thrust  horse  power 
delivered  divided  by  torque  horse  power  received.  Note  the 
curves  for  torque  and  thrust  power  in  Fig.  52 ;  a  comparison 
of  these  is  very  interesting. 

It  has  been  found  that  efficiency  depends  upon  the  ratio 
V  IN  and  not  upon  the  absolute  values  of  V  or  N;  if  V  and  N 


38 


are  both  changed  in  the  same  proportion,  efficiency  remains 
unchanged.  Furthermore,  in  comparing  propellers  of  the 
same  design  but  with  different  diameters  D,  it  is  found  that 
efficiency  depends  not  upon  V  /N  but  upon  V  /ND,  namely, 
the  effective  pitch  ratio  which  varies  with  the  slip.  Propeller 
efficiencies  are,  therefore,  plotted  for  various  values  of 
V  /ND  or  for  various  values  of  slip.  Both  scales  are 
shown  in  Fig.  55. 

Referring  to  Fig.  5 5,  and  to  Fig.  52  which  relates  to  the 
same  propeller,  it  is  seen  that  when  V  /ND  =  o,  correspond- 
ing to  100  per  cent,  slip,  thrust  power  is  zero  and  hence 
propeller  efficiency  is  zero.  As  V  /ND  increases,  propeller 
efficiency  increases  until  a  maximum  efficiency  of  80  per 
cent.,  or  so,  is  reached.  As  V /ND  is  further  increased,  the 
efficiency  decreases,  and  again  becomes  zero  when  V  /ND 
reaches  a  certain  value  (the  dynamic  pitch  ratio  of  the 
propeller)  corresponding  to  zero  thrust  and  zero  slip.  It  is 
seen,  from  Fig.  55,  that  this  propeller  has  a  dynamic  pitch 
ratio  1.2,  whereas  the  nominal  pitch  ratio  is  0.9. 

Every  propeller  has  an  efficiency  curve  of  the  type  shown  in 
Fig.  55.  It  is  seen  that  for  a  given  number  of  revolutions 
per  minute  there  is  a  certain  airplane  velocity  V,  or  for  a 
given  airplane  velocity  V  there  is  a  certain  number  of  pro- 
peller revolutions  N,  at  which  the  efficiency  of  a  particular 
propeller  is  a  maximum. 

A  propeller  should,  accordingly,  be  selected*  that  has  high 


"The  same  care  in  selection  has  to  be  taken  in  case  of  a  marine  propel- 
ler. Take  as  an  illustration  two  tug  boats,  with  identical  hulls  and 
engines,  but  different  propellers.  One  boat,  with  propeller  that  gives 
full  power  when  travelling  at  high  velocity,  far  outstrips  the  other  in  the 
race  to  an  incoming  steamer,  but  when  it  comes  to  pulling  a  load  it  is 
inferior  to  the  other  boat  equipped  with  a  propeller  that  gives  full 
power  when  travelling  at.  low  velocity. 


39 

efficiency  and  power  at  the  operating  values  of  V  and  N. 
A  propeller  that  is  very  good  for  a  certain  airplane  and  engine 
may  be  very  poor  for  another  airplane  or  engine.  In  other 
words,  the  propeller,  engine  and  plane  must  fit,  so  that, 
each  will  be  operating  under  good  conditions. 

It  is  well  to  operate  a  propeller  at  a  value  of  V  /ND  some- 
what lower  (rather  than  higher)  than  the  value  of  maximum 
efficiency,  in  order  to  obtain  greater  power.  The  points  for 
maximum  power*  and  maximum  efficiency  are  marked  on  the 
curve.  As  already  stated,  maximum  efficiency  occurs  when 
the  slip  is,  say,  25  to  40  per  cent.,  and  maximum  power 
when  the  slip  is,  say,  40  to  50  per  cent. 

A  wide  range  of  high  efficiency  is  usually  more  desirable 
than  a  narrower  range  of  slightly  higher  efficiency. 

Pitch  ratio  and  efficiency. 

The  efficiency  curves  for  three  propellers  with  different 
pitch  ratios  but  otherwise  similar  are  shown  in  Fig.  56. 
The  nominal  pitch  ratios  of  the  three  propellers  are  0.5,  0.7, 
and  0.9;  the  dynamic  pitch  ratios  (shown  by  the  values  of 
V/ND  when  the  efficiency  curves  fall  to  zero)  are  0.76,  0.96 
and  1.2,  respectively.  Which  propeller  is  the  best  to  use  is 
seen  to  depend  upon  what  is  the  value  of  V/ND  under  work- 
ing conditions.  Thus,  when  V/ND  is  less  than  0.47,  the 
propeller  with  pitch  ratio  0.5  is  seen  to  be  the  most  efficient 
of  the  three;  when  V/ND  is  more  than  .052,  this  same 
propeller  is  the  least  efficient. 

Pitch  ratio  and  power. 

Pitch  ratio  does  not  affect  efficiency  alone.     In  Fig.  57  are 


"The   point    for     maximum    power  depends    upon    D    and    pitch 
ratio.     The  point  is  marked  here  for  D  =  8'  9"  and  pitch  ratio  =  0.9. 


40 


shown  curves  of  thrust  power  for  the  same  three  propellers, 
having  nominal  pitch  ratios  0.5,  0.7  and  0.9.  It  is  seen  that 
for  maximum  power,  as  well  as  for  maximum  efficiency,  the 
value  of  V  /ND  must  be  greater  for  the  propeller  of  greater 
pitch.  For  the  three  propellers  here  shown,  maximum  power 
is  seen  to  increase  with  pitch  ratio,  but  this  is  true  only  for  a 
limited  range  of  pitch  ratio 

Combined  engine  and  propeller  characteristics. 

We  have  discussed  various  propeller  characteristics 
independent  of  the  motor  used  to  drive  the  propeller,  the 
separate  study  of  engine  and  propeller  being  for  most  pur- 
poses preferable.  Thus,  in  Fig.  53,  was  shown  the  thrust 
horse  power  obtained  from  a  certain  propeller  driven  at 
specified  constant  speeds  by  any  motor.  This  constant 
speed  is  obtained  by  throttle  adjustment,  when  a  gas  engine 
is  used. 

In  Fig.  58  are  shown  curves  for  thrust  horse  power  for  a 
given  propeller  driven  by  a  particular  gas  engine,  these 
curves  being  not  for  constant  speed  as  in  Fig.  53,  but  for 
constant  throttle. 

It  was  shown  in  Fig.  50  how  the  brake  horse  power  and 
speed  N  is  determined  for  full  throttle  (or  for  ^  or  y£  throttle) 
when  F  is  50,  7  5 , 100, 1 2  5  or  1 50  M  P  H.  Thrust  horse  power 
may  be  obtained  by  multiplying  brake  horse  power,  as  here 
shown,  by  efficiency,  which  is  known  from  Fig.  55  when  V, 
N  and  D  are  known.  The  curves  in  Fig.  58  were  thus 
determined. 

The  chief  propeller  characteristics  have  now  been  shown, 
most  important  being  the  power  available  curves  in  Fig.  53, 
useful  for  direct  comparison  with  curves  of  power  required. 

Let  us  now  examine  briefly  the  basis  for  propeller  theory. 


41 


120 


100 


40 


2QO     400    600     800    1000    1200    t+00 
SPEED,  REVOLUTIONS  PER  MINUTE 


Fig.  46.  Torque  horse  power  required  to  drive  a  particular  pro- 
peller at  different  speeds  (revolutions  per  minute)  when 
travelling  through  the  air  at  50,  100  and  150  M  P  H.,  at  ground 
level.  Propeller  diameter,  8'  9";  pitch  ratio,  0.9.  Maximum 
propeller  efficiency  is  at  m. 


43 


tso 

100 
75 
50 
25 


20       40.        GO        QO         100       1.20       14-0 
VELOCITY,    MILES  PER  HOUR. 


Fig.  47.  Variation  of  propeller  torque  horse  power  with  velocity 
when  propeller  is  driven  at  constant  speed.  Same  data  as  Fig. 
46.  Maximum  efficiency  at  m. 


45 


120 

100 


S.60 

Ul 

1  40 


20 


m. 


200       4-00       GOO        QOO       1000        1200     KOO 
SPEED,,  REVOLUTIONS  PER  MINUTE 


Fig.  48.  Speed  N  and  power,  of  particular  engine  and  propeller, 
determined  by  intersection  of  curves  for  engine  brake  horse  power 
and  propeller  torque  horse  power. 


47 


120 


80 


GO 


40 


20 


0         200        400         600        800         1000       1200       WO 
SPEED  ,  REVOLUTIONS  PER  MJNUTE 


Fig.  49.  Speed  N',  N"  and  N'"  and  corresponding  power,  for 
particular  engine  and  propeller,  determined  for  three  different 
amounts  of  engine  throttle,  when  velocity  is  100  MPH. 


120 


100 


80 


60 


40 


20 


200       400        £00        800      1000       1200 
SPEED ,  REVOLUTIONS  PER  MIMUTE 


1400 


Fig.  50.  Curves  for  engine  brake  horse  power  for  different  amounts 
of  throttle  and  propeller  torque  horse  power  for  different  veloci- 
ties. Intersections  determines  speed  and  power  for  each  velocity 
and  amount  of  throttle.  Maximum  efficiency  at  m. 


51 


1000 

800 


§500 

£ 

17400 


200 


0          20          40          GO         80         100        120         140 
VELOCITY,  MILES  PER.  HOUR. 


Fig.  51.  Variation  of  thrust  with  velocity,  for  a  particular  pro- 
peller, when  driven  at  constant  speed.  Pitch  ratio  0.9,  diameter 
8' 9'. 


53 


'  0  20  40  CO  60  100          120          HO 

VELOCITY,  MILES  PER  HOUR 

90      80       70      CO       50      40      30       20       10        0 
PERCENT  SLIP 


Fig.  52.  Variation  of  thrust  horse  power  with  velocity  for  a  parti- 
cular propeller  when  driven  at  1200  R.  P.  M.  Dotted  curves 
show  thrust  and  velocity.  The  upper  curve,  reproduced  from 
Fig.  47,  shows  torque  horse  power. 


55 


230 
180 


0  20          40  60          BO          100          120         140          160 

COWSLIP  VELOCITY,  MILES  PER  HOUR 


Fig.  53.  Curves  for  thrust  horse  power  (usually  called  power 
available)  for  particular  propeller  driven  at  different  speeds  N, 
by  any  engine.  Maximum  propeller  efficiency  is  at  m. 


57 


220 
ISO 

1 120 

580 

^40 

0 


40         CQ          80          100         120        H-0 
VELOCITY ,  MILES  PER  HOUR 


Fig.  54.  Thrust  horse  power  of  similar  propellers  with  different 
diameters,  at  constant  speed  N  =  1200  R.  P.  M.  Pitch  ratio 
0.9.  Maximum  efficiency  at  m. 


\ 


59 


0'80 


5040 
u. 
& 
Q'20 


0'2 


0-8 


ro 


100    SO     80     70      £0     50     40     30      20       10 
PERCENT  SLIP 


Fig.  55.  Propeller  efficiency  for  different  values  of  V/ND.  Effi- 
ciency is  equal  to  thrust  horse  power  divided  by  torque  horse 
power;  see  Fig.  52.  Pitch  ratio,  0.9.  Values  for  V,  N  or  D 
are  not  fixed. 


61 


•0-60 


Ui 


020 


Fig.   56.     Efficiency   of   three  similar   propellers   with   different 
pitch  ratios. 


63 


IJ20 
100 


20        40        60        80        100       1-20 
VELOCITY,  MILES  PER  HOUR 


Fig.  57.  Thrust  horse  power  of  three  similar  propellers  with 
different  pitch  ratios.  Point  of  maximum  efficiency  is  marked 
byx. 


65 


O.    50 

UJ 

g 

140 
J- 

00 

2    20 


0  25  50  75  100  US  150 

VELOCITY,  MILES  PER  HOUR. 


Fig.  58.  Combined  engine  and  propeller  characteristic.  Thrust 
horse  power,  or  power  available,  for  constant  throttle;  a  par- 
ticular propeller  (pitch  ratio  0.9,  diameter  8'  9")  driven  by  a 
particular  engine.  Maximum  efficiency  at  m.  For  engine 
curves,  see  Fig.  45. 


67 


(d)     Propeller  Theory 

The  foregoing  discussion  of  the  characteristics  of  a  pro- 
peller in  operation  shows  working  results  in  simple  form; 
these  are  the  facts  that  can  be  easily  understood,  independent 
of  any  theory  that  may  be  used  to  explain  them. 
~T  The  oldest  theory  of  the  propeller  treats  it  as  a  screw,  which 
moves  forward  as  it  turns,  and  upon  this  conception  are  based 
many  propeller  terms  in  common  use.  In  an  incompressible 
fluid,  as  water,  the  screw  theory  is  fairly  satisfactory  and  the 
marine  propeller  is,  accordingly,  commonly  treated  as  a  screw. 
When,  however,  the  medium  is  air,  that  can  be  compressed 
and  rarefied  as  any  gas  and  has  a  density  only  i  /8oo  the 
density  of  water,  the  screw  theory  is  far  from  satisfactory 
and,  as  a  theory  for  the  air  propeller,  has  been  practically 
abandoned. 


Aerofoil  theory  of  the  propeller. 

The  most  satisfactory  theory  of  the  air  propeller  considers 
the  propeller  blade  as  a  rotating  aerofoil.  When  the  propel- 
ler is  merely  rotating  and  has  no  forward  velocity,  each  ele- 
ment of  the  blade  moves  in  a  circle,  the  plane  of  rotation  being 
perpendicular  to  the  propeller  shaft.  When  the  propeller 
makes  N  revolutions  per  minute,  the  velocity  of  rotation 
of  any  element  at  a  distance  r  feet  from  the  center  of  the  shaft 
is  2  ic  r  N  feet  per  minute. 

In  flight  the  propeller  has  a  forward  velocity  in  addition 
to  its  rotation,  and  the  path  of  any  element  is  a  cork-screw 
curve  or  helix  and  not  a  circle.  The  velocity  of  any  element 
along  this  path  is  then  the  resultant  of  its  forward  velocity  V 
and  its  velocity  of  rotation,  2  x  r  N. 

Fig.  59  shows  the  plan  of  a  propeller  blade  and  several 
sections  at  different  distances  from  the  center.  The 


68 

similarity  of  these  sections  to  the  section  of  an  airplane  wing 
and  the  justification  of  the  aerofoil  theory  is  obvious. 

Fig.  60  is  an  illustrative  diagram  (not  to  scale)  of  one  sec- 
tion of  a  propeller  blade,  developing  more  fully  the  aerofoil 
theory.  Each  section  or  "element"  of  the  blade  may  thus 
be  treated  as  an  aerofoil. 

The  angle  of  incidence  i,  at  which  any  blade  element  or 
section  attacks  the  relative  air  due  to  its  motion,  is  the  angle 
between  the  chord  of  the  element  and  its  resultant  flight 
path,  as  shown  in  Fig.  60. 

The  blade  angle  or  pitch  angle  (nominal  or  structural 
pitch  angle)  for  any  particular  section  is  the  angle  a  between 
its  chord  and  the  direction  of  its  rotation  in  a  plane  perpendi- 
cular to  the  propeller  shaft.  As  shown  in  the  previous  figure, 
this  angle  decreases  for  the  various  sections  of  a  blade  as  we 
proceed  from  hub  or  boss  to  tip;  that  is,  the  blade  angle  a 
decreases*  as  the  distance  r  from  the  hub  increases. 

When  a  propeller  is  rotating,  but  has  no  forward  velocity, 
its  motion  is  in  the  plane  of  rotation  and  the  angle  of  incidence 
of  a  blade  element  is  obviously  equal  to  the  pitch  angle  a,  for 
this  is  then  the  angle  at  which  the  blade  element  attacks  the 
relative  air  due  to  its  rotation. 

In  flight,  when  there  is  a  forward  velocity  V,  the  resultant 
motion  or  flight  path  of  a  blade  element  is  a  helix  and  the 
angle  of  incidence  of  a  blade  element  with  the  relative  wind 
is  the  angle  i  between  its  chord  and  this  heliacal  path.  OP, 
in  Fig.  60,  shows  a  short  portion  of  this  path.  It  will  be  seen 
that  as  the  forward  velocity  V  increases  (relative  to  N)  the  angle 
of  blade  incidence  decreases. 


^Determination  of  pitch  from  propeller  measurement. — The  tangent  of  a 
is  equal  to  the  structural  pitch  divided  by  2  v  r.  The  structural  pitch 
of  a  propeller  is,  accordingly,  equal  to  2  IT  r  tan  a  and  can  be  determined 
by  measuring  the  pitch  angle  at  any  distance  r  from  the  hub. 


DIRECTION    OF    ROTATION 


Fig.  59.     Plan  and  section  of  propeller  blade. 


71 


The  effective  pitch  angle,  as  shown  in  the  figure,  is  the 
angle  e  which  the  resultant  flight  path  makes  with  the  plane 
of  rotation.  The  effective  pitch  angle  varies  with  different 
conditions  of  operation  and  increases  as  V /N  increases,  the 
tangent  of  e  being  equal  to  F/2  x  r  N.  The  effective  pitch 
angle  thus  determines  the  forward  travel  of  the  propeller  per 
revolution.  The  effective  pitch  angle  and  effective  pitch  are 
zero  when  V  =  o,  corresponding  to  100  per  cent,  slip  and 
maximum  thrust;  the  angle  of  blade  incidence  is  then  a 
maximum  and  the  thrust  is  a  maximum. 

Lift  and  drag. — As  in  the  case  of  any  aerofoil,  each  blade 
element  has  a  lift  perpendicular  to,  and  a  drag  or  resistance 
in  the  direction  of,  the  flight  path.  The  direction  of  L  and  D 
are  indicated  in  the  diagram.  Their  values  are 

Lift  =  L  =  KLSVR2; 
Drag  =  D  =  KDSVR2. 

Here  S  is  the  area  of  the  blade  element ;  FR  its  resultant 
velocity  along  its  heliacal  path;  KL  and  KD  are  the  usual 
coefficients  which  depend  upon  aerofoil  shape  and  vary 
with  the  angle  of  blade  incidence. 

Thrust  and  torque. — The  component  of  force  parallel  to 
the  shaft  of  the  propeller  gives  thrust;  the  component  of 
force  in  the  direction  of  rotation  gives  torque.  Although 
thrust  results  from  lift,  it  is  seen  that  thrust  is  not  precisely 
equal  to  lift ;  nor  is  torque  precisely  equal  to  drag. 

The  total  thrust  and  torque  for  the  propeller  as  a  whole 
is  the  sum  of  the  thrust  and  torque  of  the  separate  blade 
elements. 

Angle  of  blade  incidence. — The  angle  of  incidence  i  varies 
during  flight  from,  say,  2°  or  3°  in  horizontal  flight  to,  say,  10° 
or  perhaps  1 2  °  in  climbing .  As  the  angle  of  incidence  increases 


72 


(with  an  increase  in  slip  and  decrease  in  V /N)  the  lift,  and  so 
the  thrust*,  increases.  The  increase  in  thrust,  with  increase 
in  slip  and  decrease  in  V/N,  has  been  shown  by  the  curve 
in  Fig.  5 1 .  This  increase,  in  climbing,  may  be  obtained  by 
a  decrease  in  V  or  an  increase  in  N,  or  both. 

Negative  blade  incidence  for  zero  thrust. — As  the  angle  of 
incidence  decreases  (with  decrease  of  slip  and  increase  of 
V/N)  the  lift,  and  so  the  thrust,  decreases;  but  at  zero 
incidence  there  is  still  some  lift  and  thrust.  As  with  any 
aerofoil  there  is  a  certain  negative  incidence  at  which  there 
is  no  lift  (as  shown  in  Fig.  n,  pagef  18),  so  with  a  propeller 
element  there  is  a  certain  negative  incidence  at  which  there  is 
no  thrust.  The  resultant  path  of  a  blade  element  is  then  as 
indicated  by  the  dotted  line  OF  in  Fig.  60,  in  advance  of  the 
chord  of  the  blade  element,  instead  of  back  of  it  as  shown  by 
OP  for  positive  incidence. 

The  angle  between  OF  (the  resultant  path  for  zero  thrust) 
and  the  direction  of  rotation  OB,  is  the  dynamic  pitch  angle, 
and  the  corresponding  pitch  is  the  dynamic  pitch. 

To  obtain  positive  thrust,  the  effective  pitch  angle  e  must 
be  less  than  the  dynamic  pitch  angle,  by  an  amount  dependent 
upon  the  slip.t 

L/D  ratio  for  propeller. — The  L/D  ratio  for  a  propeller 
section  has  a  maximum  value  of  about  20,  when  the  blade 
incidence  is,  say,  4°  or  5°.  It  is  sought  in  propeller  design 


"Thrust  is  equal  to  the  component  of  L  parallel  to  the  shaft,  less  the 
component  of  D  in  that  direction.  Torque  is  the  sum  of  the  compon- 
ents of  L  and  D  in  the  plane  of  rotation.  Thus, 

Thrust  =  L  cos  e  —  D  sin  e. 

Torque  =  L  sin  e  +  D  cos  e. 

fSee  "Airplane  Characteristics." 

JSlip  varies  as  the  difference  between  the  tangents  of  the  two  angles. 


100%  SLIP  D 


DIRECTION      Or     ROTATION 

IN    PLANE 
PERPENDICULAR       TO     SHAFT 


Fig.  60.  Particular  section  of  propeller  blade  at  distance  of  r  from 
center  of  shaft,  showing  the  behavior  of  a  propeller  blade  as  an 
aerofoil,  attacking  the  air  at  an  angle  of  incidence  i. 


75 


and  operation  to  approach  a  maximum  value  in  this  ratio 
(or  rather  in  the  thrust /torque  ratio)  but  there  are  limita- 
tions in  structure  that  make  this  difficult. 

Blade  shape. 

The  problem  of  determining  the  several  sections  for  a  pro- 
peller blade  is  much  the  same  as  that  of  determining  the 
section  for  any  aerofoil,  although  there  are  differences  due 
to  the  heliacal  path  in  one  case  and  the  straight  path  in  the 
other,  and  consequent  differences  in  the  eddies  and  vortices 
produced. 

The  front  surface  of  a  propeller  blade  (the  upper  surface, 
considered  as  an  aerofoil  in  the  usual  manner)  is  highly 
cambered.  The  amount  of  this  camber  and  its  distribution 
depends  somewhat  upon  the  intended  service.  The  back 
surface  is  flat,  or  nearly  so,  for  it  is  found  that  there  is  little  or 
no  gain  in  shaping  this  surface.  Aspect  ratio  enters  in  blade 
design  much  as  in  the  design  of  any  aerofoil.  To  obtain  the 
advantage  of  high  aspect  ratio,  a  long  and  narrow  blade  is 
used  for  an  air  propeller.  (Not  so  for  a  marine  propeller.) 

The  greatest  thrust  and  torque  in  a  propeller  blade  is 
obtained  toward  the  tip,  the  maximum  being  about  4  /$  the 
way  from  hub  to  tip. 

Mechanical  strength  is  an  important  consideration  in  pro- 
peller design.  Changes  in  blade  shape,  that  produce  little 
change  in  aerod^Tiamic  efficiency,  may  have  a  large  effect 
upon  strength.  In  fact  in  propeller  design  the  question  of 
strength  is  foremost.  Particularly  true  is  this  as  the  hub  is 
approached,  for  this  part  of  the  propeller — on  account  of  its 
lesser  velocity  of  rotation — contributes  little  to  thrust,  so  that 
strength  is  here  practically  the  entire  problem.  High  polish 
is  given  the  blade  to  reduce  resistance.  The  surface  is  given 


76 


a  waterproof  finish  to  avoid  absorption  of  moisture  and  con- 
sequent warping. 

Very  important  is  a  proper  propeller  balance,  a  slight 
unbalancing  at  high  velocities  of  rotation  causing  forces  that 
soon  become  destructive. 


Uniform  and  variable  pitch ;  mean  pitch. 

When  a  propeller  is  constructed  with  the  same  pitch  at 
all  parts,  from  hub  to  tip,  the  pitch  is  said  to  be  uniform. 
When  the  pitch  varies  from  hub  to  tip,  the  pitch  is  said  to 
be  variable.  A  mean  value  for  pitch  is  then  sometimes 
given,  but  the  determination  of  mean  pitch  is  somewhat 
arbitrary.  It  has  been  found  that  a  variable  pitch  gives  no 
^  gain  in  aerodynamic  efficiency. 

1    Scientific  basis  of  aerofoil  theory. 

-* 
The  aerofoil  theory  has  put  the  theory  of  the  propeller  on 

a  scientific  basis  and  has  removed  much  that  was  formerly 
mysterious  or,  at  least,  not  well  understood.  Recourse, 
of  course,  must  be  made  to  experiment  for  fundamental 
data,  but  when  the  theory  is  understood  these  experiments 
may  be  made  systematically  and  not  blindly. 

Although  a  knowledge  of  the  working  characteristics  of  the 
propeller  is  all  that  is  needed  for  many  purposes,  some 
knowledge  of  the  theory  of  the  propeller  as  an  aerofoil  proves 
a  valuable  aid  in  explaining  its  behavior  under  different 
conditions  and  in  understanding  the  relations  between  the 
f  various  quantities  involved  in  its  operation?]  The  foregoing 
discussion,  prepared  primarily  for  this  purpose,  should  also 
serve  as  a  general  introduction  to  a  more  detailed  study  of  the 
propeller,  either  practical  or  theoretical. 


APPENDIX 
GLOSSARY* 

AEROFOIL:  A  winglike  structure,  flat  or  curved,  designed 
to  obtain  reaction  upon  its  surface  from  the  air  through 
which  it  moves. 

AEROPLANE  :    See  Airplane. 

AILERON:  A  movable  auxiliary  surface  used  to  produce  a 
rolling  moment  about  the  fore-and-aft  axis. 

AIRCRAFT:  Any  form  of  craft  designed  for  the  navigation 
of  the  air — airplanes,  balloons,  dirigibles,  helicopters,  kites, 
kite  balloons,  ornithopters,  gliders,  etc. 

AIRPLANE:  A  form  of  aircraft  heavier  than  air  which  has 
wing  surfaces  for  support  in  the  air,  with  stabilizing  sur- 
faces, rudders  for  steering,  and  power  plant  for  propulsion 
through  the  air.  This  term  is  commonly  used  in  a  more 
restricted  sense  to  refer  to  air-planes  fitted  with  landing 
gear  suited  to  operation  from  the  land.  If  the  landing 
gear  is  suited  to  operation  from  the  water,  the  term  "sea- 
plane" is  used.  (See  definition.) 

Pusher. — A  type  of  airplane  with  the  propeller  in  the 

rear  of  the  engine. 
Tractor. — A  type  of  airplane  with  the  propeller  in  front 

of  the  engine. 

AIR-SPEED  METER:  An  instrument  designed  to  measure  the 
speed  of  an  aircraft  with  reference  to  the  air. 

ALTIMETER  :  An  aneroid  mounted  on  an  aircraft  to  indicate 
continuously  its  height  above  the  surface  of  the  earth. 

ANEMOMETER  :  Any  instrument  for  measuring  the  velocity 
of  the  wind. 


*From  Report  No.  15,  on  "Nomenclature  for  Aeronautics,"  by  the 
National  Advisory  Committee  for  Aeronautics. 

77 


78 


ANGLE: 

Of  attack  or  of  incidence  of  an  aerofoil. — The  acute  angle 
between  the  direction  of  the  relative  wind  and  the 
chord  of  an  aerofoil;  i.  e.,  the  angle  between  the  chord 
of  an  aerofoil  and  its  motion  relative  to  the  air. 
(This  definition  may  be  extended  to  any  body  having 
an  axis.) 

Critical. — The  angle  of  attack  at  which  the  hit-curve  has 
its  first  maximum;  sometimes  referred  to  as  the 
"burble  point."  (If  the  "lift  curve"  has  more  than 
one  maximum,  this  refers  to  the  first  one.) 

Gliding. — The  angle  the  flight  path  makes  with  the  hori- 
zontal when  flying  in  still  air  under  the  influence  of 
gravity  alone,  i.  e.,  without  power  from  the  engine. 

APPENDIX:  The  hose  at  the  bottom  of  a  balloon  used  for 
inflation.  In  the  case  of  a  spherical  balloon  it  also  serves 
for  equalization  of  pressure. 

ASPECT  RATIO  :    The  ratio  of  span  to  chord  of  an  aerofoil. 

AVIATOR:  The  operator  or  pilot  of  heavier-than-air  craft. 
This  term  is  applied  regardless  of  the  sex  of  the  operator. 

AXES  OF  AN  AIRCRAFT:  Three  fixed  lines  of  reference; 
usually  centroidal  and  mutually  rectangular. 

The  principal  longitudinal  axis  in  the  plane  of  symmetry, 
usually  parallel  to  the  axis  of  the  propeller,  is  called  the  fore 
and  aft  axis  (or  longitudinal  axis) ;  the  axis  perpendicular 
to  this  in  the  plane  of  symmetry  is  called  the  vertical  axis; 
and  the  third  axis,  perpendicular  to  the  other  two,  is  called 
the  transverse  axis  (or  lateral  axis).  In  mathematical 
discussions  the  first  of  these  axes,  drawn  from  front  to  rear, 
is  called  the  X  axis;  the  second,  drawn  upward,  the  Z  axis; 
and  the  third,  forming  a  "left-handed"  system,  the  Y  axis. 

BALANCING  FLAPS  :    See  Aileron. 

BALLONET:  A  small  balloon  within  the  interior  of  a  balloon 
or  dirigible  for  the  purpose  of  controlling  the  ascent  or 
descent,  and  for  maintaining  pressure  on  the  outer  envelope 
so  as  to  prevent  deformation.  The  ballonet  is  kept  inflated 


79 


with  air  at  the  required  pressure,  under  the  control  of  a 
blower  and  valves. 

BALLOON:  A  form  of  aircraft  comprising  a  gas  bag  and  a 
basket.  The  support  in  the  air  results  from  the  buoyancy 
of  the  air  displaced  by  the  gas  bag,  the  form  of  which  is 
maintained  by  the  pressure  of  a  contained  gas  lighter  than 
air. 
Barrage. — A  small  spherical  captive  balloon,  raised  as  a 

protection  against  attacks  by  airplanes. 
Captice. — A  balloon  restrained  from  free  flight  by  means 

of  a  cable  attaching  it  to  the  earth. 
Kite. — An  elongated  form  of  captive  balloon,  fitted  with 
tail  appendages  to  keep  it  headed  into  the  wind,  and 
deriving  increased  lift  due  to  its  axis  being  inclined  to 
the  wind. 
Pilot. — A  small  spherical  balloon  sent  up  to  show  the 

direction  of  the  wind. 

Sounding. — A  small  spherical  balloon  sent  aloft,  without 
passengers,  but  with  registering  meteorological  instru- 
ments. 

BALLOON  BED  :  A  mooring  place  on  the  ground  for  a  captive 
balloon. 

BALLOON  CLOTH:  The  cloth,  usually  cotton,  of  which 
balloon  fabrics  are  made. 

BALLOON  FABRIC  :  The  finished  material,  usually  rubberized, 
of  which  balloon  envelopes  are  made. 

BANK:  To  incline  an  airplane  laterally — i.  e.,  to  roll  it  about 
the  fore  and  aft  axis.  Right  bank  is  to  incline  the  airplane 
with  the  right  wing  down  Also  used  as  a  noun  to  describe 
the  position  of  an  airplane  when  its  lateral  axis  is  inclined 
to  the  horizontal. 

BAROGRAPH:  An  instrument  used  to  record  variations  in 
barometric  pressure.  In  aeronautics  the  charts  on  which 
the  records  are  made  indicate  altitudes  directly  instead  of 
barometric  pressures. 


80 


BASKET:  The  car  suspended  beneath  a  balloon,  for  passen- 
gers, ballast,  etc. 

BIPLANE :  A  form  of  airplane  in  which  the  main  supporting 
surface  is  divided  into  two  parts,  one  above  the  other. 

BODY  OF  AN  AIRPLANE:  The  structure  which  contains  the 
power  plant,  fuel,  passengers,  etc. 

BONNET  :  The  appliance,  having  the  form  of  a  parasol,  which 
protects  the  valve  of  a  spherical  balloon  against  rain. 

BRIDLE:  The  system  of  attachment  of  cable  to  a  balloon, 
including  lines  to  the  suspension  band. 

BULLSEYES:  Small  rings  of  wood,  metal,  etc.,  forming  part 
of  balloon  rigging,  used  for  connection  or  adjustment  of 
ropes. 

BURB LE  POINT  :    See  Angle,  critical. 

CABANE  :  A  pyramidal  framework  upon  the  wing  of  an  air- 
plane, to  which  stays,  etc.,  are  secured. 

CAMBER:  The  convexity  or  rise  of  the  curve  of  an  aerofoil 
from  its  chord,  usually  expressed  as  the  ratio  of  t  he  maxi- 
mum departure  of  the  curve  from  the  chord  to  the  length 
of  the  chord.  "Top  camber"  refers  to  the  top  surface  of  an 
aerofoil,  and  "bottom  camber"  to  the  bottom  surface; 
"mean  camber"  is  the  mean  of  these  two. 

CAPACITY:    See  Load. 

The  cubic  contents  of  a  balloon. 

CENTER  :  Of  pressure  of  an  aerofoil. — The  point  in  the  plane 
of  the  chords  of  an  aerofoil,  prolonged  if  necessary,  through 
which  at  any  given  attitude  the  line  of  action  of  the 
resultant  air  force  passes.  (This  definition  may  be 
extended  to  any  body.) 

CHORD: 

Of  an  aerofoil  section. — A  right  line  tangent  at  the  front 
and  rear  to  the  under  curve  of  an  aerofoil  section. 

Length. — The  length  of  the  chord  is  the  length  of  the  pro- 
jection of  the  aerofoil  section  on  the  chord. 


81 


CLINOMETER:    See  Inclinometer. 

CONCENTRATION  RING:  A  hoop  to  which  are  attached  the 
ropes  suspending  the  basket. 

CONTROLS  :  A  general  term  applying  to  the  means  provided 
for  operating  the  devices  used  to  control  speed,  direction  of 
flight,  and  attitude  of  an  aircraft 

CONTROL  COLUMN:  The  vertical  lever  by  means  of  which 
certain  of  the  principal  controls  are  operated,  usually 
those  for  pitching  and  rolling. 

CROW'S  FOOT:  A  system  of  diverging  short  ropes  for  dis- 
tributing the  pull  of  a  single  rope. 

DECALAGE:  The  angle  between  the  chords  of  the  principal 
and  the  tail  planes  of  a  monopolane.  The  same  term  may 
be  applied  to  the  corresponding  angle  between  the  direction 
of  the  chord  or  chords  of  a  biplane  and  the  direction  of  a 
tail  plane.  (This  angle  is  also  sometimes  known  as  the 
longitudinal  V  of  the  two  planes.) 

DIHEDRAL  IN  AN  AIRPLANE  :  The  angle  included  at  the  inter- 
section of  the  imaginary  surfaces  containing  the  chords  of 
the  right  and  left  wings  (continued  to  the  plane  of  symme- 
try if  necessary).  This  angle  is  measured  in  a  plane  per- 
pendicular to  that  intersection.  The  measure  of  the 
dihedral  is  taken  as  90°  minus  one-half  of  this  angle  as 
denned. 

The  dihedral  of  the  upper  wing  may  and  frequently  does 
differ  from  that  of  the  lower  wing  in  a  biplane. 
DIRIGIBLE  :    A  form  of  balloon,  the  outer  envelope  of  which 
is  of  elongated  form,  provided  with  a  propelling  system, 
car,  rudders,  and  stabilizing  surfaces. 

Nonrigid. — A  dirigible  whose  form  is  maintained  by  the 
pressure  of  the  contained  gas  assisted  by  the  car- 
suspension  system. 
Rigid. — A  dirigible  whose  form  is  maintained  by  a  rigid 

structure  contained  within  the  evnelope. 
Semirigid. — A  dirigible  whose  form  is  maintained  by 
means  of  a  rigid  keel  and  by  gas  pressure. 


82 


DIVING  RUDDER:    See  Elevator. 

DOPE  :  A  general  term  applied  to  the  material  used  in  treat- 
ing the  cloth  surface  of  airplane  members  and  balloons  to 
increase  strength,  produce  tautness,  and  act  as  a  filler  to 
maintain  air-tightness;  it  usually  has  a  cellulose  base. 

DRAG:  The  component  parallel  to  the  relative  wind  of  the 
total  force  on  an  aircraft  due  to  the  air  through  which  it 
moves. 

That  part  of  the  drag  due  to  the  wings  is  called  "wing 
resistance"  (formerly  called  "drift");  that  due  to  the  rest 
of  the  airplane  is  called  "parasite  resistance"  (formerly 
called  "head  resistance"). 

DRIFT:  See  Drag.  Also  used  as  synonymous  with  "lee- 
way," q.  v. 

DRIFT  METER:  An  instrument  for  the  measurement  of  the 
angular  deviation  of  an  aircraft  from  a  set  course,  due  to 
cross  winds. 

DRIP  CLOTH:  A  Curtain  around  the  equator  of  a  balloon, 
which  prevents  rain  from  dripping  into  the  basket. 

ELEVATOR  :  A  hinged  surface  for  controlling  the  longitudinal 
attitude  of  an  aircraft;  i.  e.,  its  rotation  about  the  trans- 
verse axis. 

EMPANNAGE  :    See  Tail. 

ENTERING  EDGE  :  The  foremost  edge  of  an  aerofoil  or  pro- 
peller blade. 

ENVELOPE:  The  portion  of  the  balloon  or  dirigible  which 
contains  the  gas. 

EQUATOR:  The  largest  horizontal  circle  of  a  spherical 
balloon. 

FINS  :  Small  fixed  aerofoils  attached  to  different  parts  of  air- 
craft, in  order  to  promote  stability;  for  example,  tail  fins, 
skid  fins,  etc.  Fins  are  often  adjustable.  They  may  be 
either  horizontal  or  vertical. 

FLIGHT  PATH  :  The  path  of  the  center  of  gravity  of  an  air- 
craft with  reference  to  the  earth. 


83 

FLOAT  :  That  portion  of  the  landing  gear  of  an  aircraft  which 
provides  buoyancy  when  it  is  resting  on  the  surface  of  the 
water. 

FUSELAGE  :    See  Body. 

GAP  :  The  shortest  distance  between  the  planes  of  the  chords 
of  the  upper  and  lower  wings  of  a  biplane. 

G A  s  B  A  G  :    See  Envelope . 

GLIDE  :     To  fly  without  engine  power. 

GLIDER  :  A  form  of  aircraft  similar  to  an  airplane,  but  with- 
out any  power  plant. 

When  utilized  in  variable  winds  it  makes  use  of  the  soar- 
ing principles  of  flight  and  is  sometimes  called  a  soaring 
machine. 

GORE  :   One  of  the  segments  of  fabric  composing  the  envelope. 

GROUND  CLOTH  :  Canvas  placed  on  the  ground  to  protect  a 
balloon. 

GUIDE  ROPE  :  The  long  trailing  rope  attached  to  a  spherical 
balloon  or  dirigible,  to  serve  as  a  brake  and  as  a  variable 
ballast. 

GUY:  A  rope,  chain,  wire,  or  rod  attached  to  an  object  to 
guide  or  steady  it,  such  as  guys  to  wing,  tail,  or  landing  gear. 

HANGAR:    A  shed  for  housing  balloons  or  airplanes. 

HELICOPTER  :  A  form  of  aircraft  whose  support  in  the  air  is 
derived  from  the  vertical  thrust  of  propellers. 

HORN:  A  short  arm  fastened  to  a  movable  part  of  an  air- 
plane, serving  as  a  lever-arm,  e.  g.,  aileron-horn,  rudder- 
horn,  elevator-horn. 

INCLINOMETER:  An  instrument  for  measuring  the  angle 
made  by  any  axis  of  an  aircraft  with  the  horizontal,  often 
called  a  clinometer. 

INSPECTION  WINDOW:  A  small  transparent  window  in  the 
envelope  of  a  balloon  or  in  the  wing  of  an  airplane  to  allow 
inspection  of  the  interior. 


84 


KITE:  A  form  of  aircraft  without  other  propelling  means 
than  the  towline  pull,  whose  support  is  derived  from  the 
force  of  the  wind  moving  past  its  surface. 

LANDING  GEAR:  The  understructure  of  an  aircraft  designed 
to  carry  the  load  when  resting  on  or  running  on  the  surface 
of  the  land  or  water. 

LEADING  EDGE:    See  Entering  edge. 

LEEWAY  :  The  angular  deviation  from  a  set  course  over  the 
earth,  due  to  cross  currents  of  wind,  also  called  drift; 
hence,  "drift  meter." 

LIFT:  The  component  perpendicular  to  the  relative  wind, 
in  a  vertical  plane,  of  the  force  on  an  aerofoil  due  to  the  air 
pressure  caused  by  motion  through  the  air. 

LIFT  BRACING  :    See  Stay. 

LOAD: 

Dead. — The  structure,  power  plant,  and  essential  acces- 
sories of  an  aircraft. 

Full. — The  maximum  weight  which  an  aircraft  can  sup- 
port in  flight;  the  "gross  weight." 

Useful. — The  excess  of  the  full  load  over  the  dead-weight 
of  the  aircraft  itself,  *'.  e.,  over  the  weight  of  its  struc- 
ture, power  plant,  and  essential  accessories.  (These 
last  must  be  specified.) 

LOADING  :    See  Wing,  loading. 

LOBES  :    Bags  at  the  stern  of  an  elongated  balloon  designed 
to  give  it  directional  stability. 

LONGERON:    See  Longitudinal. 

LONGITUDINAL  :  A  fore-and-aft  member  of  the  framing  of  an 
air-plane  body,  or  of  the  floats,  usually  continuous  across  a 
number  of  points  of  support. 

MONOPLANE  :  A  form  of  airplane  whose  main  supporting  sur- 
face is  a  single  wing,  extending  equally  on  each  sideof  the  body. 

MOORING  BAND  :  The  band  of  tape  over  the  top  of  a  balloon 
to  which  are  attached  the  mooring  ropes. 


85 


NACELLE:    See  Body.     Limited  to  pushers. 

NET:  A  rigging  made  of  ropes  and  twine  on  spherical  bal- 
loons, which  supports  the  entire  load  carried. 

ORNITHOPTER:  A  form  of  aircraft  deriving  its  support  and 
propelling  force  from  flapping  wings. 

PANEL:  The  unit  piece  of  fabric  of  which  the  enevelope  is 
made. 

PARACHUTE  :  An  apparatus,  made  like  an  umbrella,  used  to 
retard  the  descent  of  a  falling  body. 

PATCH  SYSTEM:  A  system  of  construction  in  which  patches 
(or  adhesive  flaps)  are  used  in  place  of  the  suspension  band. 

PERMEABILITY.  The  measure  of  the  loss  of  gas  by  diffusion 
through  the  intact  balloon  fabric. 

PITOT  TUBE  :  A  tube  with  an  end  open  square  to  the  fluid 
stream,  used  as  a  detector  of  an  impact  pressure.  It  is 
usually  associated  with  a  coaxial  tube  surrounding  it, 
having  perforations  normal  to  the  axis  for  indicating  static 
pressure;  or  there  is  such  a  tube  placed  near  it  and  parallel 
to  it,  with  a  closed  conical  end  and  having  perforations  in 
its  side.  The  velocity  of  the  fluid  can  be  determined  from 
the  difference  between  the  impact  pressure  and  the  static 
pressure,  as  read  by  a  suitable  gauge.  This  instrument  is 
often  used  to  determine  the  velocity  of  an  aircraft  through 
the  air. 

PONTOONS  :    See  Float. 

PUSHER  :    See  Airplane. 

PYLON  :    A  mast  or  pillar  serving  as  a  marker  of  a  course. 

RACE  OF  A  PROPELLER:    See  Slip  stream. 

RELATIVE  WIND:  The  motion  of  the  air  with  reference  to  a 
moving  body.  Its  direction  and  velocity,  therefore,  are 
found  by  adding  two  vectors,  one  being  the  velocity  of  the 
air  with  reference  to  the  earth,  the  other  being  equal  and 
opposite  to  the  velocity  of  the  body  with  reference  to  the 
earth. 


86 


RIP  CORD  :  The  rope  running  from  the  rip  panel  of  a  balloon 
to  the  basket,  the  pulling  of  which  causes  immediate 
deflation. 

RIP  PANEL  :  A  strip  in  the  upper  part  of  a  balloon  which  is 
torn  off  when  immediate  deflation  is  desired. 

RUDDER:  A  hinged  or  pivoted  surface,  usually  more  or  less 
flat  or  stream  lined,  used  for  the  purpose  of  controlling  the 
attitude  of  an  aircraft  about  its  "vertical"  axis,  i.  e.,  for 
controlling  its  lateral  movement. 

Rudder  bar. — The  foot  bar  by  means  of  which  the  rudder 
is  operated. 

SEAPLANE  :  A  particular  form  of  airplane  in  which  the  land- 
ing gear  is  suited  to  operation  from  the  water. 

SERPENT  :    A  short,  heavy  guide  rope. 

SIDE  SLIPPING  :  Sliding  downward  and  inward  when  making 
a  turn;  due  to  excessive  banking.  It  is  the  opposite  of 
skidding. 

SKIDDING:  Sliding  sideways  away  from  the  center  of  the 
turn  in  flight.  It  is  usually  caused  by  insufficient  banking 
in  a  turn,  and  is  the  opposite  of  side  slipping. 

SKIDS  :  Long  wooden  or  metal  runners  designed  to  prevent 
nosing  of  a  land  machine  when  landing  or  to  prevent  drop- 
ping into  holes  or  ditches  in  rough  ground.  Generally 
designed  to  function  should  the  landing  gear  collapse  or 
fail  to  act. 

SLIP  STREAM  OR  PROPELLER  RACE  :  The  stream  of  air  driven 
aft  by  the  propeller  and  with  a  velocity  relative  to  the  air- 
plane greater  than  that  of  the  surrounding  body  of  still  air. 

SOARING  MACHINE  :    See  Glider. 

SPAN  OR  SPREAD  :  The  maximum  distance  laterally  from  tip 
to  tip  of  an  airplane  wing,  or  the  lateral  dimension  of  an 
aerofoil. 


87 


STABILITY  :  A  quality  in  virtue  of  which  an  airplane  in  flight 
tends  to  return  to  its  previous  attitude  after  a  slight  dis- 
turbance. 

Directional. — Stability  with  reference  to  the  vertical  axis. 

Dynamical. — The  quality  of  an  aircraft  in  flight  which 
causes  it  to  return  to  a  condition  of  equilibrium  after 
its  attitude  has  been  changed  by  meeting  some  dis- 
turbance, e.  g.,  a  gust.  This  return  to  equilibrium  is 
due  to  two  factors;  first,  the  inherent  righting 
moments  of  the  structure;  second,  the  damping  of 
the  oscillations  by  the  tail,  etc. 

Inherent. — Stability  of  an  aircraft  due  to  the  disposition 
and  arrangement  of  its  fixed  parts — i.  e.,  that  property 
which  causes  it  to  return  to  its  normal  attitude  of 
flight  without  the  use  of  the  controls. 

Lateral. — Stability  with  reference  to  the  longitudinal  (or 
fore  and  aft)  axis. 

Longitudinal. — Stability  with  reference  to  the  lateral 
axis. 

Statical. — In  wind  tunnel  experiments  it  is  found  that 
there  is  a  definite  angle  of  attack  such  that  for  a  greater 
angle  or  a  less  one  the  righting  moments  are  in  such  a 
sense  as  to  tend  to  make  the  attitude  return  to  this 
angle.  This  holds  true  for  a  certain  range  of  angles  on 
each  side  of  this  definite  angle;  and  the  machine  is 
said  to  possess  "statical  stability"  through  this  range. 

STABILIZER:  Any  device  designed  to  steady  the  motion  of 
aircraft. 

STAGGER:  The  amount  of  advance  of  the  entering  edge  of 
the  upper  wing  of  a  biplane  over  that  of  the  lower,  expressed 
as  percentage  of  gap;  it  is  considered  positive  when  the 
upper  surface  is  forward. 

STALLING:  A  term  describing  the  condition  of  an  airplane 
which  from  any  cause  has  lost  the  relative  speed  necessary 
for  control. 


88 


STATOSCOPE:  An  instrument  to  detect  the  existence  of  a 
small  rate  of  ascent  or  descent,  principally  used  in  balloon- 
ing. 

STAY  :  A  wire,  rope,  or  the  like  used  as  a  tie  piece  to  hold 
parts  together,  or  to  contribute  stiffness;  for  example,  the 
stays  of  the  wing  and  body  trussing. 

STEP  :    A  break  in  the  form  of  the  bottom  of  a  float. 

STREAM-LINE  FLOW:  A  term  in  hydromechanics  to  describe 
the  condition  of  continuous  flow  of  a  fluid,  as  distinguished 
from  eddying  flow. 

STREAM-LINE  SHAPE:    A  shape  intended  to  avoid  eddying 
and  to  preserve  stream-line  flow. 

STRUT:  A  compression  member  of  a  truss  frame;  for 
instance,  the  vertical  members  of  the  wing  truss  of  a 
biplane. 

SUSPENSION  BAND  :  The  band  around  a  balloon  to  which  are 
attached  the  basket  and  the  main  bridle  suspensions. 

SUSPENSION  BAR:  The  bar  used  for  the  concentration  of 
basket  suspension  ropes  in  captive  balloons. 

SWEEP  BACK:  The  horizontal  angle  between  the  lateral  axis 
of  an  airplane  and  the  entering  edge  of  the  main  planes. 

TAIL:  The  rear  portion  of  an  aircraft,  to  which  are  usually 
attached  rudders,  elevators,  stabilizers,  and  fins. 

TAIL  CUPS:  The  steadying  device  attached  at  the  rear  of 
certain  types  of  elongated  captive  balloons. 

THIMBLE  :  An  elongated  metal  eye  spliced  in  the  end  of  a 
rope  or  cable. 

TRACTOR:    See  Airplane. 

TRAILING  EDGE:  The  rearmost  edge  of  an  aerofoil  or  pro- 
peller blade. 

TRIPLANE:  A  form  of  airplane  whose  main  supporting  sur- 
face is  divided  into  three  parts,  superimposed. 


89 


TRUSS:  The  framing  by  which  the  wing  loads  are  trans- 
mitted to  the  body ;  comprises  struts,  stays,  and  spars. 

UNDERCARRIAGE  :    See  Landing  gear. 

WARP  :    To  change  the  form  of  the  wing  by  twisting  it. 

WASH  OUT:  A  permanent  warp  of  an  aerofoil  such  that  the 
angle  of  attack  decreases  toward  the  wing  tips. 

WEIGHT:    Gross.     See  Load,  full. 

WINGS  :    The  main  supporting  surfaces  of  an  airplane. 

WING  FLAP:    See  Aileron. 

WING  LOADING:  The  weight  carried  per  unit  area  of  sup- 
porting surface. 

WING  MAST  :  The  mast  structure  projecting  above  the  wing, 
to  which  the  top  load  wires  are  attached. 

WING  RIB:  A  fore-and-aft  member  of  the  wing  structure 
used  to  support  the  covering  and  to  give  the  wing  section 
its  form. 

WING  SPAR  OR  WING  BEAM:  A  transverse  member  of  the 
wing  structure. 

YAW  :    To  swing  off  the  course  about  the  vertical  axis. 

Angle  of. — The  temporary  angular  deviation  of  the  fore- 
and-aft  axis  from  the  course. 


91 


POWER  REQUIRED 


92 


MINIMUM  VELOCITY 


40  40  eo  eo  iqo- 

VELOCITY  -  -  MILES  PER  HOUR 


39-     Required  power  at   different   velocities,   when 
=  20001bs.;  W/S  =  6;   parasite  resistance  =0.04^. 


0  20  40  6C  80  100 

VELOCITY  -  -  MILES  PER   HOUR 


Fig.  40.  Variation  of  required  power  with  velocity. 
The  three  curves  show  effect  of  changing  weight 
(W  —  1000,  2000  and  3000  Ibs.)  when  loading  is  kept 
constant  (W/S  =  6);  parasite  resistance  =  0.04  F2. 


94 


20  40  SO  80  1OO 

VELOCITY  -  -  MILES  PER  HOUR 


Fig.  41.  Variation  of  required  power  with  velocity. 
The  three  curves  show  effect  of  changing  loading 
(W/S  =  4,  6  and  8)  when  weight  is  kept  constant 
(W  =  2000  Ibs.);  parasite  resistance  =  0.047*. 


95 


140 


w 
o 

**      50 

I 

§       ,0 


20  40  60  80  100 

VELOCITY  -  -  MILES  PER  HOUR 


Fig.  42.  Variation  of  required  power  with  velocity. 
The  three  curves  show  effect  of  changing  weight 
(W  =  1333,  2000  and  2666  Ibs.)  and  loading  in  propor- 
tion (W/S  =  4,  6  and  8),  wing-area  :being  constant; 
parasite  resistance  =  0.04  F2. 


96 


20  4J>  60  89  100 

VELOCITY  -  -  MILES  PER  HOUR 


Fig.  43.  Variation  of  required  power  with  velocity. 
The  three  curves  show  effect  of  changing  parasite  re- 
sistance (R  =  0.02  F2,  R  =  0.04  F2  and  R  =  0.06  F2); 
weight  and  loading  constant  (W  =  2000  Ibs.;  W/S  =  6). 


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